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Kähler Geometry of the Space of Knots

  • Jean-Luc Brylinski
Part of the Progress in Mathematics book series (MBC)

Abstract

Let M be a smooth, paracompact, oriented manifold of dimension n. We introduce the free loop space LM of smooth maps S 1M. We will identify S 1 with ℝ/ℤ and denote by x the parameter in ℝ/ℤ. First, recall from [P-S] how the space LM of smooth loops S 1M is made into a smooth manifold, modelled on the topological vector space C (S 1,ℝ n ). This vector space has the structure of an ILH space (inverse limit of Hilbert spaces) in the sense of §1.4.

Keywords

Vector Field Vector Bundle Tangent Vector Normal Bundle Coadjoint Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Jean-Luc Brylinski
    • 1
  1. 1.Department of MathematicsThe Penn State UniversityUniversity ParkUSA

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