Equivariant Khovanov Homotopy Type and Periodic Links

dc.contributor.advisorLipshitz, Robert
dc.contributor.authorMusyt, Jeffrey
dc.date.accessioned2019-09-18T19:33:01Z
dc.date.available2019-09-18T19:33:01Z
dc.date.issued2019-09-18
dc.description.abstractIn this thesis, we give two equivalent definitions for a group $G$ acting on a strictly-unitary-lax-2-functor $D:\CC\rightarrow\mathscr{B}$ from the cube category to the Burnside category. We then show that the natural $\mathbb{Z}/p\mathbb{Z}$ action on a $p$-periodic link $L$ induces such an action on Lipshitz and Sarkar's Khovanov functor $F_{Kh}(L): \CC \rightarrow \mathscr{B}$ which makes the Khovanov homotopy type $\mathcal{X}(L)$ into an equivariant knot invariant. That is, if a link $L'$ is equivariantly isotopic to $L$, then $\mathcal{X}(L')$ is Borel homotopy equivalent to $\mathcal{X}(L)$.en_US
dc.identifier.urihttps://hdl.handle.net/1794/24956
dc.language.isoen_US
dc.publisherUniversity of Oregon
dc.rightsAll Rights Reserved.
dc.subjectKhovanov Homologyen_US
dc.subjectKnot Theoryen_US
dc.subjectLow-Dimensional Topologyen_US
dc.titleEquivariant Khovanov Homotopy Type and Periodic Links
dc.typeElectronic Thesis or Dissertation
thesis.degree.disciplineDepartment of Mathematics
thesis.degree.grantorUniversity of Oregon
thesis.degree.leveldoctoral
thesis.degree.namePh.D.

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