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)

 

Half De Rham complexes and line fields
on odd-dimensional manifolds


Author: Houhong Fan
Journal: Trans. Amer. Math. Soc. 348 (1996), 2947-2982
MSC (1991): Primary 57R25, 57M99; Secondary 57R80, 58F25, 58A12
MathSciNet review: 1357879
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we introduce a new elliptic complex on an odd-dimensional manifold with a self-dual line field. The notion of a self-dual line field is a generalization of the notion of a conformal line field. Ellipticity, Fredholm properties and Hodge decompositions of these new complexes are proved both in the case of a closed manifold and in the case of a manifold with boundary. The cohomology groups of these elliptic complexes are computed in some cases. In addition, in this paper, we generalize the notion of an anti-self-dual connection on a smooth 4-manifold to a 3-manifold with a line field and a smooth 5-manifold with a line field. The above new elliptic complexes can be twisted by anti-self-dual connections in dimensions 3 and 5, but only by flat connections in dimensions above 5. This reveals a special feature of dimensions 3 and 5.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 57R25, 57M99, 57R80, 58F25, 58A12

Retrieve articles in all journals with MSC (1991): 57R25, 57M99, 57R80, 58F25, 58A12


Additional Information

Houhong Fan
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520
Email: hhfan@math.yale.edu.

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01661-3
PII: S 0002-9947(96)01661-3
Received by editor(s): March 23, 1995
Received by editor(s) in revised form: November 6, 1995
Article copyright: © Copyright 1996 American Mathematical Society