An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds

Zeidler, Rudolf

doi:10.2140/agt.2017.17.3081

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds

Rudolf Zeidler

Algebraic & Geometric Topology 17 (2017) 3081–3094

DOI: 10.2140/agt.2017.17.3081

Abstract

We exhibit geometric situations where higher indices of the spinor Dirac operator on a spin manifold $N$ are obstructions to positive scalar curvature on an ambient manifold $M$ that contains $N$ as a submanifold. In the main result of this note, we show that the Rosenberg index of $N$ is an obstruction to positive scalar curvature on $M$ if $N ↪ M ↠ B$ is a fiber bundle of spin manifolds with $B$ aspherical and $π_{1} (B)$ of finite asymptotic dimension. The proof is based on a new variant of the multipartitioned manifold index theorem which might be of independent interest. Moreover, we present an analogous statement for codimension-one submanifolds. We also discuss some elementary obstructions using the $\hat{A}$ -genus of certain submanifolds.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/agt

We have not been able to recognize your IP address 3.237.2.4 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

positive scalar curvature, multipartitioned manifolds, coarse index theory, asymptotic dimension, aspherical manifolds

Mathematical Subject Classification 2010

Primary: 58J22

Secondary: 46L80, 53C23

References

Publication

Received: 3 November 2016

Revised: 6 February 2017

Accepted: 26 February 2017

Published: 19 September 2017

Authors

Rudolf Zeidler
Mathematisches Institut Westfälische Wilhelms-Universität Münster Münster Germany
http://wwwmath.uni-muenster.de/u/rudolf.zeidler/

Volume 17, issue 5 (2017)