scholarly journals Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants

2021 ◽  
Author(s):  
Boris Botvinnik ◽  
◽  
Paolo Piazza ◽  
Jonathan Rosenberg ◽  
◽  
...  
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar

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 On Gromov’s conjecture for totally non-spin manifolds

2016 ◽  
Vol 08 (04) ◽  
pp. 571-587
Author(s):  
Dmitry Bolotov ◽  
Alexander Dranishnikov
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Universal Covering ◽  
Positive Scalar Curvature ◽  
Fundamental Groups ◽  
Closed Formula ◽  
Duality Group ◽  
Positive Scalar ◽  
Spin Manifolds ◽  
Stability Conjecture

Gromov’s conjecture states that for a closed [Formula: see text]-manifold [Formula: see text] with positive scalar curvature, the macroscopic dimension of its universal covering [Formula: see text] satisfies the inequality [Formula: see text] [9]. We prove that for totally non-spin [Formula: see text]-manifolds, the inequality [Formula: see text] implies the inequality [Formula: see text]. This implication together with the main result of [6] allows us to prove Gromov’s conjecture for totally non-spin [Formula: see text]-manifolds whose fundamental group is a virtual duality group with [Formula: see text]. In the case of virtually abelian groups, we reduce Gromov’s conjecture for totally non-spin manifolds to the problem whether [Formula: see text]. This problem can be further reduced to the [Formula: see text]-stability conjecture for manifolds with free abelian fundamental groups.

On Gromov's positive scalar curvature conjecture for duality groups

2014 ◽  
Vol 06 (03) ◽  
pp. 397-419 ◽  
Author(s):  
Alexander Dranishnikov
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Duality Group ◽  
Positive Scalar ◽  
Universal Covers ◽  
Duality Groups

We prove the inequality [Formula: see text] for the macroscopic dimension of the universal covers [Formula: see text] of almost spin n-manifolds M with positive scalar curvature whose fundamental group π1(M) is a virtual duality group that satisfies the coarse Baum–Connes conjecture.

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
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