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Morse theory in field theory. (English) Zbl 1117.81124
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 207-220 (2007).
Summary: We describe a geometrical interpretation of Topological Quantum Mechanics (TQM). Basics of the general topological theories are briefly discussed as well. The appropriate correspondence between objects of TQM and algebraic topology is pointed out. It is proved that the correlators in TQM can be expressed via intersection numbers of some submanifolds of the target space with paths of steepest descent between critical points. Another correspondence is only conjectured, namely the correspondence between correlators and an integral of Massey products on cohomology classes of the target manifold.
MSC:
81T45Topological field theories