Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Contact reduction and groupoid actions


Authors: Marco Zambon and Chenchang Zhu
Journal: Trans. Amer. Math. Soc. 358 (2006), 1365-1401
MSC (2000): Primary 53D10, 53D20, 58H05
Published electronically: June 21, 2005
MathSciNet review: 2187657
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a new method to perform reduction of contact manifolds that extends Willett's and Albert's results. To carry out our reduction procedure all we need is a complete Jacobi map $J:M \rightarrow \Gamma_0$ from a contact manifold to a Jacobi manifold. This naturally generates the action of the contact groupoid of $\Gamma_0$ on $M$, and we show that the quotients of fibers $J^{-1}(x)$ by suitable Lie subgroups $\Gamma_x $ are either contact or locally conformal symplectic manifolds with structures induced by the one on $M$.

We show that Willett's reduced spaces are prequantizations of our reduced spaces; hence the former are completely determined by the latter. Since a symplectic manifold is prequantizable iff the symplectic form is integral, this explains why Willett's reduction can be performed only at distinguished points. As an application we obtain Kostant's prequantizations of coadjoint orbits. Finally we present several examples where we obtain classical contact manifolds as reduced spaces.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53D10, 53D20, 58H05

Retrieve articles in all journals with MSC (2000): 53D10, 53D20, 58H05


Additional Information

Marco Zambon
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: Institut für Mathematik, Universität Zürich-Irchel, 8057 Zürich, Switzerland
Email: zambon@math.unizh.ch

Chenchang Zhu
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: D-MATH, ETH-Zentrum, CH-8092 Zürich, Switzerland
Email: zhu@math.ethz.ch

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03832-8
PII: S 0002-9947(05)03832-8
Received by editor(s): May 25, 2004
Published electronically: June 21, 2005
Article copyright: © Copyright 2005 American Mathematical Society