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Bordered Floer homology and incompressible surfaces
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We show that bordered Heegaard Floer homology detects homologically essential compressing disks, and that bordered-sutured Floer homology detects partly boundary-parallel tangles and bridges, in natural ways. For example, there is a bimodule
Λ
so that the tensor product of
CFD
^
(
Y
)
and
Λ
is
Hom
-orthogonal to
CFD
^
(
Y
)
if and only if the boundary of
Y
admits a homologically 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
^
to compute bordered-sutured Floer homology, making both results on detecting essential incompressibility practical. In particular, this makes computing Zarev’s tangle invariant manifestly combinatorial.
Title: Bordered Floer homology and incompressible surfaces
Description:
We show that bordered Heegaard Floer homology detects homologically essential compressing disks, and that bordered-sutured Floer homology detects partly boundary-parallel tangles and bridges, in natural ways.
For example, there is a bimodule
Λ
so that the tensor product of
CFD
^
(
Y
)
and
Λ
is
Hom
-orthogonal to
CFD
^
(
Y
)
if and only if the boundary of
Y
admits a homologically 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
^
to compute bordered-sutured Floer homology, making both results on detecting essential incompressibility practical.
In particular, this makes computing Zarev’s tangle invariant manifestly combinatorial.
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