Tuesday Seminar on Topology

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Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KOHNO Toshitake, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya
Remarks Tea: 16:30 - 17:00 Common Room

2022/07/12

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Sungkyung Kang (Center for Geometry and Physics, Institute of Basic Science)
Cable knots and involutive Heegaard Floer homology (ENGLISH)
[ Abstract ]
Heegaard Floer homology (and its variants) carries an intrinsic symmetry, which conjecturally corresponds to the Pin(2)-equivariance in Seiberg-Witten Floer homology. By exploiting the symmetry, we prove that (odd,1)-cables of the figure-eight knots are linearly independent in the concordance group of rationally slice knots, and present a first example of rationally slice knots of complexity 1 which are not slice. Furthermore, we establish an explicit connection between involutive knot Floer theory and involutive bordered Floer theory of knot complements, and use it to prove a similar result for iterated cables of figure-eight knots. A part of this talk is based on a joint work with J. Hom, M. Stoffregen, and J. Park.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html