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Department of Mathematics] [Shinshu University] Matsumoto, 390-8621 |
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Editor of this web site; Takahiro Matsushita ---matsushita(at)shinshu-u.ac.jp |
[ Schedule ] [ Archives ] [ Algebraic Toplogy: A guide to literature ] [ Japanese ]
| Title: | Torsion in classifying spaces of gauge groups |
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| Speaker | Masaki Kameko (Shibaura Institute of Technology) |
| Room: | A-401, Faculty of Science, Shinshu University |
| Abstract: | Tsukuda showed that the integral homology of the classifying space of the gauge group of the nontrivial SO(3)-bundle over the 2-dimensional sphere has no torsion. SO(3) is isomorphic to the projective unitary group PU(2). I will generalize Tsukuda's result on the SO(3)-bundle to PU(n)-bundles. This talk is based on my paper with the same title, published online on April 1, 2024, in Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. |
| Title: | Index theory for quarter-plane Toeplitz operators via extended symbols |
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| Speaker: | Shin Hayashi (Aoyama Gakuin University) |
| Room: | A-401, Faculty of Science, Shinshu University |
| Abstract: | Index theory for Toeplitz operators on a discrete quarter-plane has been investigated by Simonenko, Douglas-Howe, Park, and index formulas are obtained by Coburn-Douglas-Singer, Duducava. In this talk, we consider such operators of two-variable rational matrix function symbols and revisit Duducavafs idea to use Gohberg-Kreinfs theory for factorizations of matrix-valued functions from a geometric viewpoint. We see that, through matrix factorizations and analytic continuations, the symbols of Fredholm quarter-plane Toeplitz operators defined originally on a two-dimensional torus can canonically be extended to some three-sphere. By using K-theory, we show that their Fredholm indices coincide with the three-dimensional winding number of extended symbols. |