Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Circle actions and scalar curvature


Author: Michael Wiemeler
Journal: Trans. Amer. Math. Soc. 368 (2016), 2939-2966
MSC (2010): Primary 53C20, 57S15
DOI: https://doi.org/10.1090/tran/6666
Published electronically: October 5, 2015
MathSciNet review: 3449263
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct metrics of positive scalar curvature on manifolds with circle actions. One of our main results is that there exist $ S^1$-invariant metrics of positive scalar curvature on every $ S^1$-manifold which has a fixed point component of codimension $ 2$. As a consequence we can prove that there are non-invariant metrics of positive scalar curvature on many manifolds with circle actions. Results from equivariant bordism allow us to show that there is an invariant metric of positive scalar curvature on the connected sum of two copies of a simply connected semi-free $ S^1$-manifold $ M$ of dimension at least six provided that $ M$ is not $ \text {spin}$ or that $ M$ is $ \text {spin}$ and the $ S^1$-action is of odd type. If $ M$ is spin and the $ S^1$-action of even type, then there is a $ k>0$ such that the equivariant connected sum of $ 2^k$ copies of $ M$ admits an invariant metric of positive scalar curvature if and only if a generalized $ \hat {A}$-genus of $ M/S^1$ vanishes.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 53C20, 57S15

Retrieve articles in all journals with MSC (2010): 53C20, 57S15


Additional Information

Michael Wiemeler
Affiliation: Institut für Mathematik, Universität Augsburg, D-86135 Augsburg, Germany
Email: michael.wiemeler@math.uni-augsburg.de

DOI: https://doi.org/10.1090/tran/6666
Keywords: Metrics of positive scalar curvature, \(S^1\)-actions
Received by editor(s): March 27, 2014
Received by editor(s) in revised form: December 16, 2014
Published electronically: October 5, 2015
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society