Fourier transforms and integer homology cobordism

Miller Eismeier, Mike

doi:10.2140/agt.2024.24.4085

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Fourier transforms and integer homology cobordism

Mike Miller Eismeier

Algebraic & Geometric Topology 24 (2024) 4085–4101

DOI: 10.2140/agt.2024.24.4085

Abstract

We explore the Fourier transform of the $d$ –invariants, which is particularly well behaved with respect to connected sum. As corollaries, we show that lens spaces are cancellable in the monoid of $3$ –manifolds up to integer homology cobordism, and we recover a theorem of González-Acuña and Short on Alexander polynomials of knots with reducible surgeries.

Keywords

lens spaces, homology cobordism, Fourier transform, Reidemeister torsion, $d$–invariant, Heegaard Floer homology

Mathematical Subject Classification

Primary: 57K31, 57R90

References

Publication

Received: 5 June 2023

Revised: 14 August 2023

Accepted: 20 August 2023

Published: 9 December 2024

Authors

Mike Miller Eismeier
Department of Mathematics and Statistics University of Vermont Burlington, VT United States

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Volume 24, issue 7 (2024)