Harvey, Shelly2017-08-032017-08-032016-052016-04-21May 2016Vance, Katherine Rose Poulsen. "Tau invariants of spatial graphs." (2016) Diss., Rice University. <a href="https://hdl.handle.net/1911/96529">https://hdl.handle.net/1911/96529</a>.https://hdl.handle.net/1911/96529In 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.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Knot theoryLink concordanceSpatial graphsHeegaard Floer homologyThesis2017-08-03