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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
© 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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