State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology

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dc.contributor.advisorCochran, Tim D.en_US
dc.creatorElliott, Andrewen_US
dc.date.accessioned2011-07-25T02:05:09Zen_US
dc.date.available2011-07-25T02:05:09Zen_US
dc.date.issued2010en_US
dc.description.abstractWe study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee's map phi. As an application, we describe a general procedure, quasipositive modification, for constructing H-thick knots in rational Khovanov homology. Moreover, we show that specific families of such knots cannot be detected by Khovanov's thickness criteria. We also exhibit a sequence of prime links related by quasipositive modification whose width is increasing.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. 2010 ELLIOTTen_US
dc.identifier.citationElliott, Andrew. "State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology." (2010) Diss., Rice University. <a href="https://hdl.handle.net/1911/62003">https://hdl.handle.net/1911/62003</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/62003en_US
dc.language.isoengen_US
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.en_US
dc.subjectMathematicsen_US
dc.titleState cycles, quasipositive modification, and constructing H-thick knots in Khovanov homologyen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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