3,210 research outputs found
Homotopy groups of the moduli space of metrics of positive scalar curvature
No full textWe show by explicit examples that in many degrees in a stable range the homotopy groups of the moduli spaces of Riemannian metrics of positive scalar curvature on closed smooth manifolds can be non-trivial. This is achieved by further developing and then applying a family version of the surgery construction of Gromov–Lawson to certain nonlinear smooth sphere bundles constructed by Hatcher
Letter of concern from Boris Drasin, President of the Jersey Homesteads Industrial Cooperative Association
No full textJersey Homesteads (later renamed the Borough of Roosevelt) was established in the 1930s as an agro-industrial cooperative community. It was established specifically for urban Jewish garment workers, many of whome had emigrated from Europe. In this letter, Boris Drasin, a community leader who was the President of the Jersey Homesteads Industrial Cooperative Association, expresses his concerns to their management corporation (Consumers Wholesale Clothiers, Inc.) about how financial losses will impact the lives of Roosevelt's residents, three-fourths of whom depended on the garment factory for their livelihoods. He makes suggestions as to how the situation might be improved
Widespread Expression of BORIS/CTCFL in Normal and Cancer Cells
No full textThis is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Positive scalar curvature on simply connected spin pseudomanifolds
No full textLet M-Sigma be an n-dimensional Thom-Mather stratified space of depth 1. We denote by beta M the singular locus and by L the associated link. In this paper, we study the problem of when such a space can be endowed with a wedge metric of positive scalar curvature. We relate this problem to recent work on index theory on stratified spaces, giving first an obstruction to the existence of such a metric in terms of a wedge alpha-class alpha(omega)(M-Sigma) is an element of KOn. In order to establish a sufficient condition, we need to assume additional structure: we assume that the link of M-Sigma is a homogeneous space of positive scalar curvature, L = G/K, where the semisimple compact Lie group G acts transitively on L by isometries. Examples of such manifolds include compact semisimple Lie groups and Riemannian symmetric spaces of compact type. Under these assumptions, when MS and beta M are spin, we reinterpret our obstruction in terms of two a-classes associated to the resolution of M-Sigma, M, and to the singular locus beta M. Finally, when M-Sigma, beta M, L and G are simply connected and dimM is big enough, and when some other conditions on L (satisfied in a large number of cases) hold, we establish the main result of this paper, showing that the vanishing of these two a-classes is also sufficient for the existence of a well-adapted wedge metric of positive scalar curvature
Boris Smolar papers, undated, 1913-1985.
No full textThis collection contains materials pertaining to the life and career of Boris Smolar, a journalist and editor-in-chief of the Jewish Telegraphic Agency and an author of children's books.Gift of Leivy Smolar
Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants
No full textIn this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space M sigma with singular stratum beta M (a closed manifold of positive codimension) and associated link equal to L, a smooth compact manifold. We briefly call such spaces manifolds with L-fibered singularities. Under suitable spin assumptions we give necessary index-theoretic conditions for the existence of wedge metrics of positive scalar curvature. Assuming in addition that L is a simply connected homogeneous space of positive scalar curvature, L = G/H, with the semisimple compact Lie group G acting transitively on L by isometries, we investigate when these necessary conditions are also sufficient. Our main result is that our conditions are indeed sufficient for large classes of examples, even when M sigma and beta M are not simply connected. We also investigate the space of such psc metrics and show that it often splits into many cobordism classes
Metrics of Positive Ricci Curvature on Connected Sums: Projective Spaces, Products, and Plumbings
No full textThe classification of simply connected manifolds admitting metrics of positive scalar curvature of initiated by Gromov-Lawson, at its core, relies on a careful geometric construction that preserves positive scalar curvature under surgery and, in particular, under connected sum. For simply connected manifolds admitting metrics of positive Ricci curvature, it is conjectured that a similar classification should be possible, and, in particular, there is no suspected obstruction to preserving positive Ricci curvature under connected sum. Yet there is no general construction known to take two Ricci-positive Riemannian manifolds and form a Ricci-positive metric on their connected sums. In this work, we utilize and extend Perelman’s construction of Ricci-positive metrics on connected sums of complex projective planes, to give an explicit construction of Ricci-positive metrics on connected sums given that the individual summands admit very specific Ricci- positive metrics, which we call core metrics. Working towards the new goal of constructing core metrics on manifolds known to support metrics of positive Ricci curvature: we show how to generalize Perelman’s construction to all projective spaces, we show that the existence of core metrics is preserved under iterated sphere bundles, and we construct core metrics on certain boundaries of plumbing disk bundles over spheres. These constructions come together to give many new examples of Ricci-positive connected sums, in particular on the connected sum of arbitrary products of spheres and on exotic projective spaces
Scalar Curvature and Transfer Maps in Spin and Spin^c Bordism
No full textIn 1992, Stolz proved that, among simply connected Spin-manifolds of dimension5 or greater, the vanishing of a particular invariant α is necessary and sufficient
for the existence of a metric of positive scalar curvature. More precisely, there is
a map α: ΩSpin → ko (which may be realized as the index of a Dirac operator) ∗
which Hitchin established vanishes on bordism classes containing a manifold with
a metric of positive scalar curvature. Stolz showed kerα is the image of a transfer
map ΩSpinBPSp(3) → ΩSpin. In this paper we prove an analogous result for Spinc- ∗−8 ∗
manifolds and a related invariant αc : ΩSpinc → ku. We show that ker αc is the ∗
sum of the image of Stolz’s transfer ΩSpinBPSp(3) → ΩSpinc and an analogous map ∗−8 ∗
ΩSpinc BSU(3) → ΩSpinc . Finally, we expand on some details in Stolz’s original paper ∗−4 ∗
and provide alternate proofs for some parts
Perturbed Special Lagrangian Submanifolds
No full textThis thesis investigates perturbed special Lagrangian submanifolds with the aim of developing a Floer theory analogous to existing theories in symplectic geometry. Special Lagrangians arise naturally in Calabi--Yau manifolds as submanifolds calibrated by the real part of the holomorphic volume form.
Following a proposal of Donaldson and Segal, we view special Lagrangians as solutions to an infinite-dimensional Lagrange multipliers problem. Perturbations of pairs of stable forms which give rise to SU(3)-structures yield perturbed special Lagrangian equations, whose solutions generalize classical special Lagrangian submanifolds.
Chapter 2 introduces a finite-dimensional Morse-theoretic model, linking the Morse homology of a constrained function to the Lagrange function of the associated Lagrange-multipliers problem. Guided loosely by analogy with the finite-dimensional case, Chapter 3 explores the Donaldosn--Segal Lagrange multipliers problem whose solutions are perturbed special Lagrangians. We prove ellipticity results, basic compactness under tameness conditions, and a natural volume bound. The main theorem is a transversality result which states that the moduli space of solutions is generically a set of isolated points
Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds
No full textLet n > 1. We prove a homological stability theorem for the
diffeomorphism groups of (4n+1)-dimensional manifolds, with respect
to forming the connected sum with (2n-1)-connected,
(4n+1)-dimensional manifolds that are stably parallelizable.
Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M.
In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds.
In addition to our main homological stability theorem, we prove several results regarding disjunction for embeddings and immersions of Z/k-manifolds that could be of independent interest
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