Daniel Ruberman
Concordance properties of parallel links.
Wed, 08/24/2011 - 15:01 — SomNambulAuthors: Daniel Ruberman, Saso Strle
Subjects: Geometric Topology
AbstractWe investigate the concordance properties of `parallel links' P(K), given by
the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to
a split link, is K necessarily slice? We show that if P(K) is smoothly
concordant to a split link, then many smooth concordance invariants of K must
vanish, including the tau and s-invariants, and suitably normalized
d-invariants of surgeries on K. We also investigate the (2,2m) cables P_m(K),
and find obstructions to smooth concordance to the sum of the (2,2m) torus link
and a split link.Double point surgery and configurations of surfaces.
Fri, 01/22/2010 - 16:01 — SomNambulAuthors: Daniel Ruberman, Hee Jung Kim
Subjects: Geometric Topology
AbstractWe introduce a new operation, double point surgery, on immersed surfaces in a
4-manifold, and use it to construct knotted configurations of surfaces in many
4-manifolds. Taking branched covers, we produce smoothly exotic actions of Z/m
x Z/n on simply connected 4-manifolds with complicated fixed-point sets.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.
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