Moduli space of nonnegatively curved metrics on manifolds of dimension 4k + 1

Dessai, Anand

doi:10.2140/agt.2022.22.325

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Moduli space of nonnegatively curved metrics on manifolds of dimension $4k+1$

Anand Dessai

Algebraic & Geometric Topology 22 (2022) 325–347

DOI: 10.2140/agt.2022.22.325

Abstract

In each dimension $4 k + 1 \geq 9$ , we exhibit infinite families of closed manifolds with fundamental group $ℤ_{2}$ for which the moduli space of metrics of nonnegative sectional curvature has infinitely many path components. Examples of closed manifolds with finite fundamental group with this property were known before only in dimension $5$ and dimensions $4 k + 3 \geq 7$ .

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Keywords

moduli spaces, nonnegative curvature, eta-invariants, diffeomorphism classification

Mathematical Subject Classification

Primary: 53C20, 58D27, 58J28

Secondary: 19K56, 53C27, 57R55

References

Publication

Received: 30 May 2020

Revised: 15 January 2021

Accepted: 9 February 2021

Published: 26 April 2022

Authors

Anand Dessai
Department of Mathematics University of Fribourg Fribourg Switzerland
https://homeweb.unifr.ch/dessaia/pub/

Volume 22, issue 1 (2022)