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The $\boldsymbol{S^1}$-Equivariant Yamabe Invariant of 3-Manifolds

Ammann, Bernd, Madani, Farid and Pilca, Mihaela (2016) The $\boldsymbol{S^1}$-Equivariant Yamabe Invariant of 3-Manifolds. International Mathematics Research Notices, rnw194.

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Other URL: http://doi.org/10.1093/imrn/rnw194


Abstract

We show that the S-1-equivariant Yamabe invariant of the 3-sphere, endowed with the Hopf action, is equal to the (non-equivariant) Yamabe invariant of the 3-sphere. More generally, we establish a topological upper bound for the S-1-equivariant Yamabe invariant of any closed oriented 3-manifold endowed with an S-1-action. Furthermore, we prove a convergence result for the equivariant Yamabe constants of an accumulating sequence of subgroups of a compact Lie group acting on a closed manifold.


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Item type:Article
Date:2016
Institutions:Mathematics > Prof. Dr. Bernd Ammann
Identification Number:
ValueType
10.1093/imrn/rnw194DOI
Keywords:SIMPLY CONNECTED MANIFOLDS; SCALAR CURVATURE; GREATER-THAN; SURGERY; 4-MANIFOLDS; SYMMETRY; METRICS; RP3;
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:39718
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