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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Contact reduction


Author: Christopher Willett
Journal: Trans. Amer. Math. Soc. 354 (2002), 4245-4260
MSC (2000): Primary 53D10, 53D20
Published electronically: May 23, 2002
MathSciNet review: 1926873
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Abstract: In this article I propose a new method for reducing co-oriented contact manifold $M$ equipped with an action of a Lie group $G$ by contact transformations. With a certain regularity and integrality assumption the contact quotient $M_\mu$ at $\mu \in \mathfrak{g}^*$ is a naturally co-oriented contact orbifold which is independent of the contact form used to represent the given contact structure. Removing the regularity and integrality assumptions and replacing them with one concerning the existence of a slice, which is satisfied for compact symmetry groups, results in a contact stratified space; i.e., a stratified space equipped with a line bundle which, when restricted to each stratum, defines a co-oriented contact structure. This extends the previous work of the author and E. Lerman.


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Additional Information

Christopher Willett
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: cwillett@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03045-3
PII: S 0002-9947(02)03045-3
Received by editor(s): November 21, 2001
Published electronically: May 23, 2002
Additional Notes: The author was supported by a National Science Foundation graduate Vertical Integration of Research and Education fellowship and the American Institute of Mathematics
Article copyright: © Copyright 2002 American Mathematical Society