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Abstract
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Ozsváth and Szabó used the knot filtration on
to define the
–invariant for knots
in the
–sphere.
We generalize their construction and define a collection of
–invariants associated
to a knot
in a rational
homology sphere
. We
then show that some of these invariants provide lower bounds for the genus of a surface with boundary
properly embedded in a
negative-definite
–manifold
with boundary
.
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Keywords
Heegaard Floer, knot invariants, genus bound, rational
homology spheres
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R58
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Publication
Received: 12 December 2016
Revised: 20 May 2019
Accepted: 8 November 2019
Published: 20 July 2020
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