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Geometric structures on loop and path spaces.

Muñoz, Vicente and Presas , Francisco (2010) Geometric structures on loop and path spaces. Proceedings of the Indian Academy of Sciences, 120 (4). pp. 417-428. ISSN 0253-4142

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Abstract

The loop Space associated to a Riemannian manifold admits a quasi-symplectic structure (that is, a closed 2-form which is non-degenerate up to a finite-dimensional kernel). We show how to construct a compatible almost-complex structure. Finally conditions to have contact structures on loop spaces are studied.

Item Type:Article
Uncontrolled Keywords:Loop space; Symplectic structures; Contact structures.
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:17010
References:

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Pressley A and Segal G, Loop groups, Oxford Mathematical Monographs, Oxford Science Publications (New York: The Clarendon Press, Oxford University Press)(1986)

Segal G, Elliptic cohomology, in: Seminaire Bourbaki 40 (1987–88), no. 695,Asterisque 161–162 (1988) 187–201

Wurzbacher T, Symplectic geometry of the loop space of a symplectic manifold,J. Geom. Phys. 16 (1995) 345–384

Deposited On:05 Nov 2012 11:32
Last Modified:07 Feb 2014 09:40

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