Geodesic
On the Whistle Cobordism Operation in String Topology of Classifying Spaces
Documenta mathematica, Tome 25 (2020), pp. 125-142
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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.
DOI : 10.4171/dm/740
Classification : 55P50, 55R35, 81T40
Mots-clés : classifying space, string topology, topological quantum field theory, Eilenberg-Moore spectral sequence 
@article{10_4171_dm_740,
     author = {Katsuhiko Kuribayashi},
     title = {On the {Whistle} {Cobordism} {Operation} in {String} {Topology} of {Classifying} {Spaces}},
     journal = {Documenta mathematica},
     pages = {125--142},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/740},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/740/}
}
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Katsuhiko Kuribayashi. On the Whistle Cobordism Operation in String Topology of Classifying Spaces. Documenta mathematica, Tome 25 (2020), pp. 125-142. doi: 10.4171/dm/740

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