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

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On prolongations of contact manifolds


Authors: Mirko Klukas and Bijan Sahamie
Journal: Proc. Amer. Math. Soc. 141 (2013), 3257-3263
MSC (2010): Primary 53D10
Published electronically: May 22, 2013
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We apply spectral sequences to derive both an obstruction to the existence of $ n$-fold prolongations and a topological classification. Prolongations have been used in the literature in an attempt to prove that every Engel structure on $ M\times \mathbb{S}^1$ with characteristic line field tangent to the fibers is determined by the contact structure induced on a cross section and the twisting of the Engel structure along the fibers. Our results show that this statement needs some modification: to classify the diffeomorphism type of the Engel structure, we additionally have to fix a class in the first cohomology of $ M$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53D10

Retrieve articles in all journals with MSC (2010): 53D10


Additional Information

Mirko Klukas
Affiliation: Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany
Email: mklukas@math.uni-koeln.de

Bijan Sahamie
Affiliation: Mathematisches Institut der LMU München, Theresienstrasse 39, 80333 München, Germany
Address at time of publication: Stanford University, 450 Serra Mall, Building 380, Stanford, California 94305
Email: sahamie@math.lmu.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11777-6
PII: S 0002-9939(2013)11777-6
Received by editor(s): August 5, 2011
Received by editor(s) in revised form: November 24, 2011
Published electronically: May 22, 2013
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2013 American Mathematical Society