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

Willis, Michael, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Krushkal, Vyacheslav, Department of Mathematics, University of Virginia

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.

PHD (Doctor of Philosophy)
Khovanov homology, Khovanov homotopy type, L-S-K spectrum, colored Khovanov homology, Jones-Wenzl projector
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