Thesis Defense Katherine Vance, Ph D Candidate

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Thesis Defense   Katherine Vance, Ph D Candidate
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Rice University Department of Mathematics says
TAU INVARIANTS OF SPATIAL GRAPHS
In 2003, Ozsvath and Szabo defined the concordance invariant Tau for knots in oriented 3-manifolds as part of the Heegaard Floer homology package. In 2011, Sarkar gave a combinatorial definition of Tau for knots in S^3 and a combinatorial proof that Tau gives a lower bound for the slice genus of a knot. Recently, Harvey and O’Donnol defined a relatively bigraded combinatorial Heegaard Floer homology theory for transverse spatial graphs in S^3 which extends knot Floer homology. We define a Z-filtered chain complex for balanced spatial graphs whose associated graded chain complex has homology determined by Harvey and O’Donnol’s graph Floer homology. We use this to show that there is a well-defined Tau invariant for balanced spatial graphs generalizing the Tau knot concordance invariant. In particular, this defines a Tau invariant for links in S^3. Using techniques similar to those of Sarkar, we show that our Tau invariant gives an obstruction to a link being slice.
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By: Rice University Department of Mathematics

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