Bordered Floer homology and incompressible surfaces

Akram Alishahi; Robert Lipshitz

doi:10.5802/aif.3276

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arXiv · 1708.05121

Bordered Floer homology and incompressible surfaces

Akram Alishahi·Robert Lipshitz

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Abstract

We show that bordered Heegaard Floer homology detects incompressible surfaces and bordered-sutured Floer homology detects partly boundary parallel tangles and bridges, in natural ways. For example, there is a bimodule Lambda so that the tensor product of CFD(Y) and Lambda is Hom-orthogonal to CFD(Y) if and only if the boundary of Y admits an essential compressing disk. In the process, we sharpen a nonvanishing result of Ni's. We also extend Lipshitz-Ozsváth-Thurston's "factoring" algorithm for computing HF-hat to compute bordered-sutured Floer homology, to make both results on detecting incompressibility practical. In particular, this makes Zarev's tangle invariant manifestly combinatorial.

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Akram Alishahi, Robert Lipshitz. 2026-05-03. Bordered Floer homology and incompressible surfaces. https://doi.org/10.5802/aif.3276

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