Geodesic
On the Whistle Cobordism Operation in String Topology of Classifying Spaces
Documenta mathematica, Tome 25 (2020), pp. 125-142.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this manuscript, we consider cobordism operations in the $2$-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.
Classification : 55P50, 81T40, 55R35
Keywords: string topology, classifying space, topological quantum field theory, Eilenberg-Moore spectral sequence 
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     author = {Kuribayashi, Katsuhiko},
     title = {On the {Whistle} {Cobordism} {Operation} in {String} {Topology} of {Classifying} {Spaces}},
     journal = {Documenta mathematica},
     pages = {125--142},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a67/}
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Kuribayashi, Katsuhiko. On the Whistle Cobordism Operation in String Topology of Classifying Spaces. Documenta mathematica, Tome 25 (2020), pp. 125-142. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a67/