TQFT string operations in open-closed string topology

Abstract

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.

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

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Cited by in corpus (2)

• Open-Closed TQFT String Operations for Disc Cobordisms, Simultaneous Saddle Interactions, and Constant Homology Classes
• String Topology, Euler Class and TNCZ free loop fibrations