τ–invariants for knots in rational homology spheres

Raoux, Katherine

doi:10.2140/agt.2020.20.1601

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

Katherine Raoux

Algebraic & Geometric Topology 20 (2020) 1601–1640

DOI: 10.2140/agt.2020.20.1601

Abstract

Ozsváth and Szabó used the knot filtration on $\hat{CF} (S^{3})$ 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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Keywords

Heegaard Floer, knot invariants, genus bound, rational homology spheres

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57R58

References

Publication

Received: 12 December 2016

Revised: 20 May 2019

Accepted: 8 November 2019

Published: 20 July 2020

Authors

Katherine Raoux
Department of Mathematics Michigan State University East Lansing, MI United States

Volume 20, issue 4 (2020)