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Homological stability for the moduli space of Riemann surfaces with boundary
No full textModuli spaces frequently arise as solutions to classification problems. Showing that a collection of objects can be given the structure of a geometric space facilitates the research of a possible parametrization on the resulting space. The goal of the present work is to prove homological stability results for the moduli space of Riemann surfaces, exclusively looking at the case of Riemann surfaces with non-empty boundary and fixed positive length at the boundary components. The reason why we restrict to such a condition can be found in the famous and often quoted article "Stability of the Homology of the Mapping Class Groups of Orientable Surfaces" published in the Annals of Mathematics by John Harer in 1985. The stability results he addresses refer to the homology of an algebraic invariant for manifolds, the so-called mapping class group. As a matter of fact, it turns out that, given a connected, compact and oriented surfaces with non-empty boundary, the
moduli space of Riemann surfaces is a model for the classifying space of the mapping class group . Therefore, under this condition, the homology of the mapping class groups of equals the homology of . The relevance of the Harer's stability theorem lies in its application in the Mumford's conjecture, formulated in 1983 by David Mumford and solved by Ib Madsen and Michael Weiss in 2007. According to the Mumford conjecture, the rational cohomology ring of the moduli space of Riemann surfaces is a polynomial algebra on the so-called Mumford-Morita-Miller classes, in a range of degrees increasing with the genus of the surface. Despite the numerous improvements of Harer's result, due to professor Nikolai V. Ivanov in 1989, Harer itself in 1993, O. Randal-Williams in 2009, and many more over a range of 35 years, variations of the paper are subjects of nowadays active research: the last attempt to improve the statement was achieved by Søren K. Boldsen in 2010 in the paper "Improved homological stability for the mapping class group with integral or twisted coefficient"; professor Nathalie Wahl reorganized all the literature concerning the stability of the mapping class groups in her paper “Homological stability for mapping class group of surfaces”, published in the third volume of the "Handbook of the moduli" in 2013
Binaries among multiple populations in the young LMC cluster NGC 2164
Get PDFUna delle scoperte più affascinanti degli ultimi anni riguarda il fatto che gli ammassi giovani di entrambe le
Nubi di Magellano sono sistemi stellari complessi. In aggiunta ad un turn-off esteso della sequenza
principale (eMSTO), comune tra gli ammassi di età intermedia, è stata osservata anche una doppia
sequenza principale (split MS). Queste scoperte hanno rivoluzionato l'idea tradizionale per cui i diagrammi
Colore-Magnitudine di questi ammassi sono simili a delle isocrone. Sono stati proposti diversi scenari per
capire l’origine dell’eMSTO e della doppia MS. I principali sono quello delle variazioni di età, per cui l’eMSTO
è il risultato di una formazione stellare prolungata, e lo scenario della rotazione, il quale assume che tutte le
stelle siano coeve ma che abbiano diverse velocità di rotazione. Nell’ambito dell’ipotesi rotazionale, il
frenamento della rotazione stellare indotto da interazioni mareali in sistemi binari sarebbe il principale
responsabile per la doppia sequenza principale.
In questa tesi sfrutto dati fotometrici di alta precisione del telescopio spaziale Hubble per determinare, per la
prima volta, la frequenza delle binarie tra le popolazioni multiple in NGC 2164. A tale scopo, applico un
nuovo metodo basato sul confronto della fotometria multi-banda delle stelle binarie con una griglia di
diagrammi simulati di binarie artificiali. La mia scoperta di una prevalenza di binarie nella sequenza
principale blu conferma il nesso fra binarie e doppia MS, e quindi supporta lo scenario relativo alla rotazione.
Riporto anche la scoperta di una nuova caratteristica nella parte alta del diagramma Colore-Magnitudine,
che suggerisce l'esistenza di una sequenza tripla
Aspetti geologici e risvolti esecutivi nella costruzione di una galleria naturale
No full textIn this script we therefore want to describe and critically comment on the construction phase of the Malo tunnel.
On the basis of construction site experience, the methods of construction of the tunnel will be exposed, highlighting the main construction site criticalities and the related measures adopted by the technical staff during the construction of the work.
Finally, in the concluding part of the script, we want to enhance the experience conducted on site, and at the same time the role played by the geologist in the construction of a tunnel, highlighting the strategic function of his professionalism in the combination of knowledge of theoretical notions with the application of the observational method, in order to classify the cluster and define its behavior
Compositional analysis of radar sounder facies along a traverse in the Martian North Polar Cap
No full textFamilies of compact complex tori
Get PDFA compact complex torus of dimension g is a complex Lie group isomorphic to V/Λ, where V is a complex vector space of dimension g and Λ is a lattice in V. Although all compact complex tori of dimension g are isomorphic in the category of real differentiable manifolds, they can have non-isomorphic structures of complex manifolds. As is common in algebraic geometry, it is possible to simplify the study of compact complex tori using a categorical approach. One possibility is through a functor F yielding an equivalence of categories between the category of compact complex tori of dimension g, and the category of triples (Λ, V, γ), where Λ is a free abelian group of rank 2g, V is a complex vector space of dimension g and γ from Λ to V is a lattice inclusion. This is important for several reasons. The first reason is that the treatment of compact complex tori under the categorical point of view allows us to focus our attention more on the relations and morphisms between them, rather than on the objects themselves. The second reason is that, since F is an equivalence, the two categories satisfy the same properties. So, in order to understand compact complex tori, it is enough to understand the category of triples (Λ, V, γ), which is an easier category to handle. The aim of this thesis is to extend F to a functor yielding an equivalence of categories between the category of families of compact complex tori of dimension g over a fixed complex manifold B, and the category of triples (Λ, V, γ), where Λ is a locally constant B-Lie group with structural group a free abelian group of rank 2g, V is a holomorphic vector bundle of rank g over B and γ from Λ to V is a morphism of B-Lie groups, such that it yields a lattice inclusion fiberwise. If B is just a point, these two categories coincide with the ones previously defined
