1,721,061 research outputs found
Similar fillings and isolation of cusps of hyperbolic 3-manifolds
No full textIn this paper we deepen the analysis of certain classes M_{g,k} of hyperbolic 3-manifolds that were introduced in a previous work by B. Martelli, C. Petronio and the author. Each element of M_{g,k} is an oriented complete finite-volume hyperbolic 3-manifold with compact connected geodesic boundary of genus g and k cusps. We study small deformations of the complete hyperbolic structure of manifolds in M_{g,k} via a close analysis of their geodesic triangulations. We prove that several elements in M_{g,k} admit non-homeomorphic hyperbolic Dehn fillings sharing the same volume, homology, cusp volume, cusp shape, Heegaard genus, complex length of the shortest geodesic, length of the shortest return path, and Turaev-Viro invariants. Manifolds which share all these invariants are called geometrically similar, and were first studied by C. D. Hodgson, R. G. Meyerhoff and J. R. Weeks. The examples of geometrically similar manifolds they described are commensurable with each other. We show here that many elements in M_{g,k} admit non-commensurable geometrically similar Dehn fillings.
The notion of geometric isolation for cusps in a hyperbolic 3-manifold was introduced by W. D. Neumann and A. W. Reid and studied by D. Calegary, who provided explanations for all the previously known examples of isolation phenomena. We show here that the cusps of any manifold M_{g,k} are geometrically isolated from each other. Apparently, isolation of cusps in our examples arises for different reasons from those described by Calegari.
We also show that any element in M_{g,k} admits an infinite family of hyperbolic Dehn fillings inducing non-trivial deformations of the hyperbolic structure on the geodesic boundary
A note on measure homology
Full text linkMeasure homology was introduced by Thurston in order to compute the simplicial volume of hyperbolic manifolds. Berlanga endowed measure homology with a structure of graded locally convex (possibly non-Hausdorff) topological vector space. In this note we completely characterize Berlanga's topology on measure homology of CW-complexes, showing in particular that it is Hausdorff. This answers a question posed by Berlanga
Hyperbolic manifolds with geodesic boundary which are determined by their fundamental group
No full textLet M and N be n-dimensional connected orientable finite-volume hyperbolic manifolds with geodesic boundary, and let f be a given isomorphism between the fundamental groups of M and N. We study the problem whether there exists an isometry between M and N which induces f.
We show that this is always the case if the dimension of M and N is at least four, while in the three-dimensional case the existence of an isometry inducing f is proved under some (necessary) additional conditions on f. Such conditions are trivially satisfied if the boundaries of M and N are both compact
An infinite family of hyperbolic graph complements in S^3
No full textFor any g>1 we construct a graph G_g in S^3 whose exterior M_g supports a complete finite-volume hyperbolic structure with one toric cusp and a connected geodesic boundary of genus g. We compute the canonical decomposition and the isometry group of M_g, showing in particular that any self-homeomorphism of M_g extends to a self-homeomorphism of the pair (S^3,G_g), and that G_g is chiral. Building on a result of Lackenby we also show that any non-meridinal Dehn filling of M_g is hyperbolic, thus getting an infinite family of graphs in S^2xS^1 whose exteriors support a hyperbolic structure with geodesic boundary
Commensurability of hyperbolic manifolds with geodesic boundary
No full textSuppose n>2, let M,M' be n-dimensional connected complete finite-volume hyperbolic manifolds with non-empty geodesic boundary, and suppose that the fundamental group of M is quasi-isometric to the fundamental group of M' (with respect to the word metric). Also suppose that if n=3, then the boundaries of M and of M' are compact. We show that M is commensurable with M'. Moreover, we show that there exist homotopically equivalent hyperbolic 3-manifolds with non-compact geodesic boundary which are not commensurable with each other.
We also prove that if M is as above and G is a finitely generated group which is quasi-isometric to the fundamental group of M, then there exists a hyperbolic manifold with geodesic boundary M'' with the following properties: M'' is commensurable with M, and G is a finite extension of a group which contains the fundamental group of M'' as a finite-index subgroup
Quasi-isometric Rigidity of Piecewise Geometric Manifolds
Full text linkTwo groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are always quasi-isometric, and a group G is quasi-isometrically rigid if every group quasi-isometric to G is virtually isomorphic to G.
In this survey we describe quasi-isometric rigidity results for fundamental groups of manifolds which can be decomposed into geometric pieces. After stating by now classical results on lattices in semisimple Lie groups, we focus on the class of fundamental groups of 3-manifolds, and describe the behaviour of quasi-isometries with respect to the Milnor-Kneser prime decomposition (following Papasoglu and Whyte) and with respect to the JSJ decomposition (following Kapovich and Leeb). We also discuss quasi-isometric rigidity results for fundamental groups of higher dimensional graph manifolds, that were recently defined by Lafont, Sisto and the author. Our main tools are the study of geometric group actions and quasi-actions on Riemannian manifolds and on trees of spaces, via the analysis of the induced actions on asymptotic cones
PAN-SPECIFIC PROBING AND SORTING OF EXTRACELLULAR NANOPARTICLES
Full text linkNanoparticelle extracellulari (eNP), comprendono le vescicole extracellulari (EV) e le lipoproteine (LP), entrambe svolgono un ruolo cruciale nella comunicazione cellula-cellula, influenzando numerosi processi fisiologici e patologici. In particolare, le EV rivestono un grande interesse nella nanomedicina, sia per la diagnostica che per la terapia, rappresentando un vasto spazio biomarcatore per le biopsie liquide. Tuttavia, le proprietà chimico-fisiche sovrapposte rendono difficile l'isolamento specifico e l'analisi accurata delle EV. Questa tesi di dottorato mira a sviluppare un metodo altamente sensibile per analizzare singole EV in biofluidi reali, con applicazioni potenziali in ambito clinico. La ricerca affronta due sfide principali nell'analisi delle eNP: il rilevamento della single EV in biofluidi complessi e la variabilità dei marcatori superficiali delle EV. Inoltre, le interazioni tra diverse eNP potrebbero portare alla formazione di complessi biologicamente rilevanti. Come parte di questo lavoro, è stata condotta un’indagine preliminare sulle interazioni tra EV e LP utilizzando tecnologie avanzate e sensibili.
Il Capitolo 2 presenta un confronto tra due piattaforme digitali altamente sensibili per l’immuno-phenotyping, fondamentali per affrontare la complessità dei fluidi bniologici. Le piattaforme basate sulle tecnologie SiMoA e SP-IRIS sono state utilizzate per sviluppare un protocollo per la valutazione delle EV, confrontandone le prestazioni in termini di sensibilità e specificità.
Il Capitolo 3 introduce il Membrane Sensing Peptide, (MSP), una sonda pan-specifica progettata per affrontare l'eterogeneità dei marcatori superficiali delle EV e consentire un'analisi imparziale delle EV. Integrato nella piattaforma SiMoA, MSP facilita l'analisi di singole EV direttamente in campioni reali, dimostrando una bassa affinità per le LP e un'elevata specificità per le EV. Questo metodo rileva le EV indipendentemente dall'espressione dei marcatori superficiali, come dimostrato con le EV derivate da globuli rossi (RBC-EVs). Dal punto di vista clinico, questo approccio ha permesso di distinguere i pazienti con infarto miocardico da quelli con angina stabile, basandosi su marcatori specifici associati alle EV presenti in siero e plasma, evidenziandone il potenziale diagnostico.
Il Capitolo 4 esplora le applicazioni di MSP, evidenziandone la versatilità sia per scopi analitici che di isolamento, senza introdurre delle variabili legati all’arricchimento di sottopopolazioni. Durante un periodo di ricerca di sei mesi presso l’ETH di Zurigo, nel gruppo del professor Arosio, MSP è stato coniugato con un polimero zwitterionico coacervato per consentire l'isolamento collettivo delle EV e fungere da “one-pot assay” per l'analisi di biomarcatori EV in fluidi complessi.
Il Capitolo 5 descrive un “approccio bottom-up” che utilizza sistemi modello (LDL, VLDL ed RBC-EVs) per studiare le interazioni EV-LP in condizioni fisiologiche. Tecnologie avanzate di immuno-affinità, tra cui Microscopie a Super-Risoluzione (SRM), Citometria a Flusso (FACS) e saggio a singola molecola (SiMoA), sono state impiegate per analizzare in dettaglio questi complessi.
In conclusione, questa tesi introduce MSP come una nuova sonda pan-specifica per le EV, offrendo un potenziale cambio di paradigma nel campo delle EV. I risultati dimostrano i vantaggi di MSP nell'analisi e nell'isolamento delle EV, così come il suo potenziale in applicazioni cliniche, aprendo la strada a test diagnostici basati sulle EV. Inoltre, è stata condotta un'indagine preliminare sulle interazioni EV-LP utilizzando tecnologie ad alta sensibilità.Extracellular nanoparticles (eNPs), including extracellular vesicles (EVs) and lipoproteins (LPs), play a crucial role in cell-to-cell communication and influence various physiological and pathological processes. Focusing on EVs, they hold particular promise in nanomedicine for diagnostics and therapeutics, representing a large biomarker space for liquid biopsies. However, overlapping of chemical-physical properties make it challenging a specific isolation, and accurate analysis of EVs. This PhD thesis aims to develop a highly sensitive method for analyzing single EV in real biofluids, with potential applications in clinical settings. The research addresses two major challenges in eNP analysis: detecting individual EV in complex biofluids and addressing EV surface marker variability. Additionally, interactions between different eNPs may lead to the formation of biologically relevant complexes. As part of this work, a preliminary investigation of EV-LP interactions was conducted using advanced, sensitive technologies.
Chapter 2 presents a comparison between two highly sensitive digital platforms for immunophenotyping, which are crucial for addressing the complexity of real biofluids. Platforms based on SiMoA and SP-IRIS technologies were used to develop a protocol for evaluating EVs, and their performance was compared in terms of sensitivity and specificity.
Chapter 3 introduces the Membrane Sensing Peptide (MSP), a pan-specific probe designed to address the heterogeneity of EV surface markers and enable unbiased EV analysis. Integrated into the SiMoA platform, MSP facilitates single EV analysis directly in real samples, demonstrating low affinity for LPs and high specificity for EVs. This method detects EVs independently of surface marker expression, as shown with Red Blood Cell-derived EVs (RBC-EVs). Clinically, this approach distinguished myocardial infarction patients from those with stable angina based on distinct EV-associated epitope signatures in serum and plasma, highlighting its diagnostic potential.
Chapter 4 explores the applications of MSP, highlighting its versatility for both analytical and isolation purposes without introducing biases related to sub-population enrichment. During a six-month research period at ETH Zurich in Professor Arosio’s group, MSP was conjugated with a zwitterionic polymer coacervate to enable collective EV isolation and serve as a "one-pot assay" for EV biomarker analysis in complex fluids.
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Chapter 5 describes a “bottom-up approach” using model systems (LDL, VLDL, and RBC-EVs) to investigate EV-LP interactions under physiological conditions. Advance immune-affinity technologies, including Super-Resolution Microscopy (SRM), Flow Cytometry (FACS), and Single Molecule Array (SiMoA), were employed to study these complexes in detail.
In conclusion, this thesis introduces MSP as a novel pan-specific EV probe, offering a potential paradigm shift in the EV field. The results demonstrate MSP’s advantages in EV analysis and isolation, as well as its potential in clinical applications, paving the way for EV-based diagnostic assays. Additionally, a preliminary investigation into EV-LP interactions was conducted using high-sensitivity technologies
Levels of knotting of spatial handlebodies
Full text linkIf H is a spatial handlebody, i.e. a handlebody embedded in the
3-sphere, a spine of H is a graph Γ ⊂ S 3 such that H is a regular neighbour-hood of Γ. Usually, H is said to be unknotted if it admits a planar spine. This suggests that a handlebody should be considered not very knotted if it admits spines that enjoy suitable special properties. Building on this remark, we define several levels of knotting of spatial handlebodies, and we provide a complete description of the relationships between these levels, focusing our attention on the case of genus 2. We also relate the knotting level of a spatial handlebody H to classical topological properties of its complement M = S 3 \ H, such as its cut number. More precisely, we show that if H is not highly knotted, then M
admits special cut systems for M , and we discuss the extent to which the converse implication holds. Along the way we construct obstructions that allow us to determine the knotting level of several families of spatial handlebodies. These obstructions are based on recent quandle–coloring invariants for spatial handlebodies, on the extension to the context of spatial handlebodies of tools coming from the theory of homology boundary links, on the analysis of appropriate coverings of handlebody complements, and on the study of the classical Alexander elementary ideals of their fundamental groups
Length functions on mapping class groups and simplicial volumes of mapping tori
Full text linkLet M be a closed orientable manifold. We introduce two numerical invariants, called filling volumes, on the mapping class group MCG(M) of M, which are defined in terms of filling norms on the space of singular boundaries on M, both with real and with integral coefficients. We show that filling volumes are length functions on MCG(M), we prove that the real filling volume of a mapping class f is equal to the simplicial volume of the corresponding mapping torus E_f, while the integral filling volume of f is not smaller than the stable integral simplicial volume of E_f.
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We discuss several vanishing and non-vanishing results for the filling volumes. As applications, we show that the hyperbolic volume of 3-dimensional mapping tori is not subadditive with respect to their monodromy, and that the real and the integral filling norms on integral boundaries are often non-biLipschitz equivalent
Integral filling volume, complexity, and integral simplicial volume of 3-dimensional mapping tori
Full text linkWe show that the integral filling volume of a Dehn twist f on a closed oriented surface vanishes, i.e., that the integral simplicial volume of the mapping torus with monodromy f
n
grows sublinearly with respect to n. We deduce a complete characterization of mapping classes on surfaces with vanishing integral filling volume and, building on results by Purcell and Lackenby on the complexity of mapping tori, we show that, in dimension three, complexity and integral simplicial volume are not Lipschitz equivalent
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