Heegaard Floer homology and the word metric on the Torelli group
Abstract
Abstract We study a relationship between the Heegaard Floer homology correction terms of integral homology spheres and the word metric on the Torelli group. For example, we use it to give a quick proof that the Cayley graph of the Torelli group has infinite diameter in the word metric induced by the generating set of all separating twists and bounding pair maps. On the other hand, we show that many subsets of the Torelli group are bounded with respect to this metric. Finally, we address the case of rational homology spheres by ruling out a certain Morita‐type formula for congruence subgroups of mapping class groups.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Combinatorial Mathematics
semigroups and automata theory
Publication details
- Journal / source
- Journal of Topology
- Volume
- 19
- Issue
- 2
- Publication date
- 16 April 2026
- Language
- EN