Charles Livingston
Topologically slice knots with nontrivial Alexander polynomial.
Tue, 01/12/2010 - 16:01 — SomNambulAuthors: Matthew Hedden, Charles Livingston, Daniel Ruberman
Subjects: Geometric Topology
AbstractLet 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.Knot 4--genus and the rank of classes in W(Q(t)).
Tue, 12/08/2009 - 16:01 — SomNambulAuthors: Charles Livingston
Subjects: Geometric Topology
AbstractTo a Seifert matrix of a knot K one can associate a matrix w(K) with entries
in the rational function field, Q(t). The Murasugi, Milnor, and Levine-Tristram
knot signatures, all of which provide bounds on the 4-genus of a knot, are
determined by w(K). More generally, the minimal rank of a representative of the
class represented by w(K) in the Witt group of hermitian forms over Q(t)
provides a lower bound for the 4-genus of K.Non-slice linear combinations of algebraic knots.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Matthew Hedden, Paul Kirk, Charles Livingston
Subjects: Geometric Topology
AbstractWe show that the subgroup of the knot concordance group generated by links of
isolated complex singularities intersects the subgroup of algebraically slice
knots in an infinite rank subgroup.Non-slice linear combinations of algebraic knots.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Matthew Hedden, Paul Kirk, Charles Livingston
Subjects: Geometric Topology
AbstractWe show that the subgroup of the knot concordance group generated by links of
isolated complex singularities intersects the subgroup of algebraically slice
knots in an infinite rank subgroup.
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