Bordered Floer homology and incompressible surfaces
arXiv:1708.05121 · doi:10.5802/aif.3276
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.
34 pages, 11 figures. V2: now also detects bridge tangles. V3: theorem numbering matches published version
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