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) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2022/11/08

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Masahiko Yoshinaga (Osaka University)
Milnor fibers of hyperplane arrangements (JAPANESE)
[ Abstract ]
A (central) hyperplane arrangement is a union of finitely many hyperplanes in a linear space. There are many relationships between the intersection lattice of the arrangement and geometry of related spaces. In this talk, we focus on the Milnor fiber of a hyperplane arrangement. The first Betti number of the Milnor fiber is expected to be determined by the combinatorial structure of the intersection lattice, however, it is still open. We discuss two results on the problem. The first (discouraging) one is concerning the dimension of (-1)-eigenspace of the monodromy action on the first cohomology group. We show that it is related to 2-torsions in the first homology of double covering of the (projectivized) complement (j.w. Ishibashi and Sugawara). The second (encouraging) one is related to the Aomoto complex, which is defined in purely combinatorial way. We show that a q-analogue of Aomoto complex determines all nontrivial monodromy eigenspaces of the Milnor fiber.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html