Fourier transforms and integer homology cobordism

Mike Miller Eismeier

doi:10.2140/agt.2024.24.4085

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arXiv · 2206.07029

Fourier transforms and integer homology cobordism

Mike Miller Eismeier

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Abstract

We explore the Fourier transform of the Heegaard Floer $d$-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 Gonz\'alez-Acu\~na--Short on Alexander polynomials of knots with reducible surgeries.

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Mike Miller Eismeier. 2022-06-14. Fourier transforms and integer homology cobordism. https://doi.org/10.2140/agt.2024.24.4085

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