Mathematical Research Letters

Volume 28 (2021)

Number 1

Heegaard Floer homology and splicing homology spheres

Pages: 93 – 106

DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n1.a4

Authors

Çağrı Karakurt (Department of Mathematics, Boğaziçi University, Bebek Istanbul, Turkey)

Tye Lidman (Department of Mathematics, North Carolina State University, Raleigh, N.C., U.S.A.)

Eamonn Tweedy (Department of Mathematics, Widener University, Chester, Pennsylvania, U.S.A.)

Abstract

We prove a basic inequality for the $d$-invariants of a splice of knots in homology spheres. As a result, we are able to prove a new relation on the rank of reduced Floer homology under maps between Seifert fibered homology spheres, improving results of the first and second authors. As a corollary, a degree one map between two aspherical Seifert homology spheres is homotopic to a homeomorphism if and only if the Heegaard Floer homologies are isomorphic.

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Ç.K. was supported by BAGEP award of the Science Academy and Boğaziçi University Research Fund Grant Number 12482.

T.L. was supported by NSF grant DMS-1709702 and a Sloan Fellowship.

Received 17 April 2019

Accepted 22 July 2019

Published 24 May 2022