Volume 20, issue 4 (2020)

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$\tau$–invariants for knots in rational homology spheres

Katherine Raoux

Algebraic & Geometric Topology 20 (2020) 1601–1640

Ozsváth and Szabó used the knot filtration on CF̂(S3) to define the τ–invariant for knots in the 3–sphere. We generalize their construction and define a collection of τ–invariants associated to a knot K in a rational homology sphere Y . We then show that some of these invariants provide lower bounds for the genus of a surface with boundary K properly embedded in a negative-definite 4–manifold with boundary Y .

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Heegaard Floer, knot invariants, genus bound, rational homology spheres
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R58
Received: 12 December 2016
Revised: 20 May 2019
Accepted: 8 November 2019
Published: 20 July 2020
Katherine Raoux
Department of Mathematics
Michigan State University
East Lansing, MI
United States