TQFT string operations in open-closed string topology

Details TQFT string operations in open-closed string topology TQFT string operations in open-closed string topology

2008-03-07

arxiv.org/abs/0803.1038v3

Mathematics

Algebraic Topology

Version 3: Minor revisions. Section 2 has been shortened. 21 pages with 13 figures

Scientific paper

To open-closed cobordism surfaces, open-closed string topology associates topological quantum field theory (TQFT) operations, namely string operations, which depend only on homeomorphism types of surfaces and which satisfy the sewing property. We show that most TQFT string operations vanish in open-closed string topology. We describe those open-closed cobordisms with vanishing string operations, and give a short list of open-closed cobordisms with possibly nontrivial string operations.

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