Affiliation:
1. School of Computer and Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
Abstract
We construct a new family of knot concordance invariants [Formula: see text], where [Formula: see text] is a prime number. Our invariants are obtained from the equivariant Seiberg–Witten–Floer cohomology, constructed by the author and Hekmati, applied to the degree [Formula: see text] cyclic cover of [Formula: see text] branched over [Formula: see text]. In the case [Formula: see text], our invariant [Formula: see text] shares many similarities with the knot Floer homology invariant [Formula: see text] defined by Hom and Wu. Our invariants [Formula: see text] give lower bounds on the genus of any smooth, properly embedded, homologically trivial surface bounding [Formula: see text] in a definite [Formula: see text]-manifold with boundary [Formula: see text].
Publisher
World Scientific Pub Co Pte Ltd
Reference18 articles.
1. Equivariant Seiberg–Witten–Floer
cohomology
2. A note on cobordisms of algebraic knots
3. Stably slice disks of links
4. M. H. Freedman and F. Quinn , Topology of 4-Manifolds, Princeton Mathematical Series, Vol. 39 (Princeton University Press, Princeton, NJ, 1990), pp. viii+259.