Fourier transforms and integer homology cobordism

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 González-Acuña--Short on Alexander polynomials of knots with reducible surgeries.

v2: Small changes. To appear in Algebraic & Geometric Topology

References in corpus (2)

• Ribbon cobordisms between lens spaces
• Cohomology jump loci of 3-manifolds