scholarly journals Moduli spaces of invariant metrics of positive scalar curvature on quasitoric manifolds

2018 ◽  
Vol 146 (10) ◽  
pp. 4521-4534
Author(s):  
Michael Wiemeler
Keyword(s):  
Scalar Curvature ◽  
Moduli Spaces ◽  
Positive Scalar Curvature ◽  
Invariant Metrics ◽  
Positive Scalar ◽  
Quasitoric Manifolds

scholarly journals On Moduli Spaces of Positive Scalar Curvature Metrics on Highly Connected Manifolds

2020 ◽  
Author(s):  
Michael Wiemeler
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Positive Scalar Curvature ◽  
Spin Manifold ◽  
Homotopy Groups ◽  
Positive Scalar ◽  
Simply Connected ◽  
Highly Connected Manifolds

Abstract Let $M$ be a simply connected spin manifold of dimension at least six, which admits a metric of positive scalar curvature. We show that the observer moduli space of positive scalar curvature metrics on $M$ has non-trivial higher homotopy groups. Moreover, denote by $\mathcal{M}_0^+(M)$ the moduli space of positive scalar curvature metrics on $M$ associated to the group of orientation-preserving diffeomorphisms of $M$. We show that if $M$ belongs to a certain class of manifolds that includes $(2n-2)$-connected $(4n-2)$-dimensional manifolds, then the fundamental group of $\mathcal{M}_0^+(M)$ is non-trivial.

scholarly journals Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

2020 ◽  
Vol 63 (4) ◽  
pp. 901-908
Author(s):  
Philipp Reiser
Keyword(s):  
Scalar Curvature ◽  
Moduli Spaces ◽  
Riemannian Metrics ◽  
Universal Cover ◽  
Positive Scalar Curvature ◽  
Spherical Space ◽  
Space Forms ◽  
Positive Scalar ◽  
Space Of Riemannian Metrics ◽  
Simply Connected

AbstractLet $M$ be a topological spherical space form, i.e., a smooth manifold whose universal cover is a homotopy sphere. We determine the number of path components of the space and moduli space of Riemannian metrics with positive scalar curvature on $M$ if the dimension of $M$ is at least 5 and $M$ is not simply-connected.

scholarly journals S1-Equivariant bordism, invariant metrics of positive scalar curvature, and rigidity of elliptic genera

2019 ◽  
Vol 12 (04) ◽  
pp. 1103-1156 ◽  
Author(s):  
Michael Wiemeler
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Spin Manifold ◽  
Invariant Metrics ◽  
Orbit Spaces ◽  
Positive Scalar ◽  
Theoretic Proof ◽  
Elliptic Genera ◽  
Previous Definition ◽  
Definition Of

We construct geometric generators of the effective [Formula: see text]-equivariant Spin- (and oriented) bordism groups with two inverted. We apply this construction to the question of which [Formula: see text]-manifolds admit invariant metrics of positive scalar curvature. It turns out that, up to taking connected sums with several copies of the same manifold, the only obstruction to the existence of such a metric is an [Formula: see text]-genus of orbit spaces. This [Formula: see text]-genus generalizes a previous definition of Lott for orbit spaces of semi-free [Formula: see text]-actions. As a further application of our results, we give a new proof of the vanishing of the [Formula: see text]-genus of a Spin manifold with nontrivial [Formula: see text]-action originally proven by Atiyah and Hirzebruch. Moreover, based on our computations we can give a bordism-theoretic proof for the rigidity of elliptic genera originally proven by Taubes and Bott–Taubes.

Positive scalar curvature metrics via end-periodic manifolds

2020 ◽  
Vol 5 (3) ◽  
pp. 639-676
Author(s):  
Michael Hallam ◽  
Varghese Mathai
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar

scholarly journals Positive scalar curvature and higher‐dimensional families of Seiberg–Witten equations

2019 ◽  
Vol 12 (4) ◽  
pp. 1246-1265
Author(s):  
Hokuto Konno
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Higher Dimensional

scholarly journals Complete hypersurfaces in cylinders

1989 ◽  
Vol 46 (2) ◽  
pp. 313-318
Author(s):  
Thomas Hasanis
Keyword(s):  
Euclidean Space ◽  
Scalar Curvature ◽  
Sectional Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Coordinate Functions ◽  
Bounded Below ◽  
Complete Hypersurfaces

AbstractWe consider the extent of certain complete hypersurfaces of Euclidean space. We prove that every complete hypersurface in En+1 with sectional curvature bounded below and non-positive scalar curvature has at least (n − 1) unbounded coordinate functions.

Minimal hypersurfaces of a positive scalar curvature manifold

1985 ◽  
Vol 190 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Sebasti�o Almeida
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Minimal Hypersurfaces ◽  
Positive Scalar

scholarly journals Einstein spaces of positive scalar curvature

1969 ◽  
Vol 3 (3-4) ◽  
pp. 457-459
Author(s):  
Yosio Mutô
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Einstein Spaces
Sign in / Sign up

Export Citation Format

Share Document