Cochran, Tim D.2011-07-252011-07-252010Elliott, 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>.https://hdl.handle.net/1911/62003We 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.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.MathematicsThesisTHESIS MATH. 2010 ELLIOTT