Topologically slice knots with nontrivial Alexander polynomial

By M. Hedden, Charles Livingston, Daniel Ruberman. 2010

61 citations recorded by the source corpus.

Let C_T be the subgroup of the smooth knot concordance group generated by topologically slice knots and let C_D be the subgroup generated by knots with trivial Alexander polynomial. We prove the quotient C_T/C_D is infinitely generated, and uncover similar structure in the 3-dimensional rational spin bordism group. Our methods also lead to the construction of links that are topologically, but not smoothly, concordant to boundary links.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f86440a33eb5ab6b58f2c8da4668f63e237bc98

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

HEEGAARD FLOER HOMOLOGY AND RATIONAL CUSPIDAL CURVES (2013, methodology): “However, in the case that a 3–manifold is of the form S(3) q (K) where q ≥ 2(genus(K)), there is a simple algorithm (originating from [20, Section 4], we use the approach of [9, 10]) to determine this invariant from CFK(K).”
The reduced knot Floer complex (2013, methodology): “These invariants have been used to answer questions related to Dehn surgery [5, 6, 19], the smooth knot concordance group [4, 11, 15, 18] and various notions of genera of knots [1, 7, 20].”
A survey on Heegaard Floer homology and concordance (2015, methodology): “t δpn is diﬃcult to compute. When Σpn(K) can described as surgery on a knot J in S3, one can use the knot Floer complex of J together with [NW10, Proposition 1.6] to compute δpn(K); see, for example, [HLR12] and [Jab12]. Moreover, similar techniques can be employed when the branched cover is surgery”
Filtering smooth concordance classes of topologically slice knots (2012, methodology): “Recent work of Hedden-LivingstonRuberman, Hom and Hedden-Kirk shows that much finer structure exists in T [34, 35, 33].”