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15 October 2020 Chern–Simons functional and the homology cobordism group
Aliakbar Daemi
Duke Math. J. 169(15): 2827-2886 (15 October 2020). DOI: 10.1215/00127094-2020-0017

Abstract

For each integral homology sphere Y , we construct a function Γ Y on the set of integers. We establish that Γ Y depends only on the homology cobordism class of Y and that it recovers the Frøyshov invariant. We state a relation between Γ Y and Fintushel and Stern’s R -invariant. We show that the value of Γ Y at each integer is related to the critical values of the Chern–Simons functional, and we give some topological applications of Γ Y . In particular, we show that if Γ Y is trivial, then there is no simply connected homology cobordism from Y to itself.

Citation

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Aliakbar Daemi. "Chern–Simons functional and the homology cobordism group." Duke Math. J. 169 (15) 2827 - 2886, 15 October 2020. https://doi.org/10.1215/00127094-2020-0017

Information

Received: 29 January 2019; Revised: 14 February 2020; Published: 15 October 2020
First available in Project Euclid: 19 September 2020

MathSciNet: MR4158669
Digital Object Identifier: 10.1215/00127094-2020-0017

Subjects:
Primary: 57R58
Secondary: 57R57

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 15 • 15 October 2020
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