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Stable Limits of the Khovanov Homology and L-S-K Spectra for Infinite Braids

Willis, Michael
Format
Thesis/Dissertation; Online
Author
Willis, Michael
Advisor
Krushkal, Vyacheslav
Abstract
We use stable limits of sequences of L-S-K spectra derived from infinite twists to define a colored L-S-K spectrum for colored links in the 3-sphere. We then prove further stabilization properties of uni-colored spectra for B-adequate links as the coloring goes to infinity, and analyze the case of the unknot in more detail. In the process we show that there are infinitely many 3-strand torus links with non-trivial Steenrod squaring action on their Khovanov homology. Finally, we also show that the limits of sequences of both Khovanov homology and L-S-K spectra derived from other positive, complete infinite braids stabilize to give the same results as those of the infinite twist.
Language
English
Published
University of Virginia, Department of Mathematics, PHD (Doctor of Philosophy), 2017
Published Date
2017-06-28
Degree
PHD (Doctor of Philosophy)
Rights
CC-BY (permitting free use with proper attribution)
Collection
Libra ETD Repository

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