An infinite-rank summand of topologically slice knots

By Jennifer Hom. 2013

53 citations recorded by the source corpus.

Let CTS be the subgroup of the smooth knot concordance group generated by topologically slice knots. Endo showed that CTS contains an infinite-rank subgroup, and Livingston and Manolescu-Owens showed that CTS contains a Z 3 summand. We show that in fact CTS contains a Z 1 summand. The proof relies on the knot Floer homology package of Ozsvath‐Szabo and the concordance invariant ". 57N70, 57R58; 57M25

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c0e0f60b41b12e472d93f09a19c68d5abbcca5a4

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Citations in the corpus

Topologically slice knots of smooth concordance order two (2012, methodology): “Recently that work has been superseded by work of Hom [18] which applies a deep analysis of the structure of Heegaard Floer complexes to construct a summand isomorphic to Z∞.”
Grid Homology for Knots and Links (2015, background): “Since B is free, the above short exact sequence dualizes to a short exact sequence of chain complexes 0 Hom(Z,K[U ]) Hom(C,K[U ]) Hom(B −1, 0 ,K[U ]) 0.”
Unoriented knot Floer homology and the unoriented four-ball genus (2015, background): “Infinitely many linearly independent homomorphisms from the smooth concordance group to Z were constructed in work of Jen Hom [6]; but previous to this work, there were a few other concordance homomorphisms that are non-trivial on topologically”
A survey on Heegaard Floer homology and concordance (2015, methodology): “See Figure 2.”
AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “By using the full knot Floer complex, one can extract additional concordance invariants; see [Hom14b, Hom15, HW14].”
More concordance homomorphisms from knot Floer homology (2019, methodology): “These knots are used in [Hom15b, Theorem 3].”
A connected sum formula for involutive Heegaard Floer homology (2016, methodology): “That group was denoted CFK in [8] and was used there to prove the existence of a Z∞ summand in the smooth concordance group of topologically slice knots, CTS .”
On the geography and botany of knot Floer homology (2014, background): “3 (CFK Geography Question) What is the image of Hom’s homomorphism H : C → CFK? In particular, is H surjective? Work of [24,35] implies that CFK (and indeed the image of H ) is necessarily infinitely generated, and has a rich filtration structure by Archimedean equivalence classes.”