On the Whistle Cobordism Operation in String Topology of Classifying Spaces

  • Katsuhiko Kuribayashi

    Department of Mathematics, Shinshu University, 3-1-1 Asahi, 390-8621 Matsumoto, Nagano, Japan
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Abstract

In this manuscript, we consider cobordism operations in the -dimensional labeled open-closed topological quantum field theory for the classifying space of a connected compact Lie group in the sense of Guldberg. In particular, it is proved that the whistle cobordism operation is non-trivial in general provided the labels are in the set of maximal closed subgroups of the given Lie group. The non-triviality of cobordism operations induced by gluing the whistle with the opposite and other labeled cobordisms is also discussed.

Cite this article

Katsuhiko Kuribayashi, On the Whistle Cobordism Operation in String Topology of Classifying Spaces. Doc. Math. 25 (2020), pp. 125–142

DOI 10.4171/DM/740