Tau invariants of spatial graphs

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dc.contributor.advisorHarvey, Shelly
dc.creatorVance, Katherine Rose Poulsen
dc.date.accessioned2017-08-03T14:38:14Z
dc.date.available2017-08-03T14:38:14Z
dc.date.created2016-05
dc.date.issued2016-04-21
dc.date.submittedMay 2016
dc.date.updated2017-08-03T14:38:14Z
dc.description.abstractIn 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.
dc.format.mimetypeapplication/pdf
dc.identifier.citationVance, 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>.
dc.identifier.urihttps://hdl.handle.net/1911/96529
dc.language.isoeng
dc.rightsCopyright 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.
dc.subjectKnot theory
dc.subjectLink concordance
dc.subjectSpatial graphs
dc.subjectHeegaard Floer homology
dc.titleTau invariants of spatial graphs
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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