Work

Bordered Floer homology, handlebody detection, and compressing diffeomorphisms

Year: 2026

Type: article

Abstract: We show that, up to connected sums with integer homology ‐spaces, bordered Floer homology detects handlebodies, as well as whether a mapping class extends over a given handlebody or compression body. Using this, we combine ideas of Casson–Long with the theory of train tracks to give an algorithm using bordered Floer homology to detect whether a mapping class extends over any compression body.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70721

Authors: Akram Alishahi, Robert Lipshitz

Institutions: University of Georgia, University of Oregon

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: National Science Foundation