Bordered Floer homology, handlebody detection, and compressing diffeomorphisms

Akram Alishahi; Robert Lipshitz

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arXiv · 2408.06619

Bordered Floer homology, handlebody detection, and compressing diffeomorphisms

Akram Alishahi·Robert Lipshitz

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Abstract

We show that, up to connected sums with integer homology $L$-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.

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Akram Alishahi, Robert Lipshitz. 2024-08-13. Bordered Floer homology, handlebody detection, and compressing diffeomorphisms. https://arxiv.org/abs/2408.06619

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