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Closed String Operators in Topology Leading to Lie Bialgebras and Higher String Algebra

In: The Legacy of Niels Henrik Abel

Author

Listed:
  • Moira Chas
  • Dennis Sullivan

Abstract

Imagine a collection of closed oriented curves depending on parameters in a smooth d-manifold M. Along a certain locus of configurations strands of the curves may intersect at certain sites in M. At these sites in M the curves may be cut and reconnected in some way. One obtains operators on the set of parametrized collections of closed curves in M. By making the coincidences transversal and compactifying, the operators can be made to act in the algebraic topology of the free loop space of M when M is oriented. The process reveals collapsing sub graph combinatorics like that for removing infinities from Feynman graphs.

Suggested Citation

  • Moira Chas & Dennis Sullivan, 2004. "Closed String Operators in Topology Leading to Lie Bialgebras and Higher String Algebra," Springer Books, in: Olav Arnfinn Laudal & Ragni Piene (ed.), The Legacy of Niels Henrik Abel, pages 771-784, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18908-1_27
    DOI: 10.1007/978-3-642-18908-1_27
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