String Topology

Abstract

Consider two families of closed oriented curves in a d-manifold. At each point of intersecction of a curve of one family with a curve of the other family, form a new closed curve by going around the first curve and then going around the second. Typically, an i-dimensional family and a j-dimensional family will produce an (i+j-d+2)-dimensional family. Our purpose is to describe mathematical structure behind such interactions.

29 pages, 8 figures

Cited by in corpus (68)

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• AP Theory II:Intrinsic 4D Quantum YM Theory with Mass Gap
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• Chen-Ruan Cohomology of cotangent orbifolds and Chas-Sullivan String Topology
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• Cyclic Homology of Fukaya Categories and the Linearized Contact Homology
• Gradation of Algebras of Curves by the Winding Number
• Orbifold String Topology