Muñoz Velazquez, 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: | Atiyah M F, Circular symmetry and stationary phase approximation, in: Colloque en honneur de Laurent Schwartz, Vol. 1, Asterisque 131 (1984) 43–59 Guest M A and Pressley A N, Holomorphic curves in loop groups, Commun. Math.Phys. 118 (1988) 511–527 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 12:32 |
| Last Modified: | 05 Nov 2012 12:32 |
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