String Topology

1999/11/21 by Moira Chas, Dennis Sullivan, Chas, Moira +1 · 3 citations
Mathematics · #17B81 #55N91 #57R19 #57R45 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:17B81 #msc:55N91 #msc:57R19 #msc:57R45

paper · pdf · doi:10.48550/arxiv.math/9911159

29 pages, 8 figures

arxiv created 1999/11/21 · arxiv updated 2009/11/30

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.

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• Gauge Symmetries, Contact Reduction, and Singular Field Theories
• String topology coproduct and Turaev cobracket on surfaces
• Quartic BV structures in supercategories and modified necklace Lie bialgebras

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