Vol. 249, No. 2, 2011

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 314: 1  2
Vol. 313: 1  2
Vol. 312: 1  2
Vol. 311: 1  2
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
String structures and canonical 3-forms

Corbett Redden

Vol. 249 (2011), No. 2, 447–484
Abstract

Using basic homotopy constructions, we show that isomorphism classes of string structures on spin bundles are naturally given by certain degree 3 cohomology classes, which we call string classes, on the total space of the bundle. Using a Hodge isomorphism, we then show that the harmonic representative of a string class gives rise to a canonical 3-form on the base space, refining the associated differential character. We explicitly calculate this 3-form for homogeneous metrics on 3-spheres, and we discuss how the cohomology theory tmf could potentially encode obstructions to positive Ricci curvature metrics.

Keywords
string structure, differential characters, positive Ricci curvature, elliptic cohomology
Mathematical Subject Classification 2000
Primary: 57R15, 58J28
Secondary: 58A14, 55N34, 53C05
Milestones
Received: 11 December 2009
Accepted: 1 July 2010
Published: 1 February 2011
Authors
Corbett Redden
Department of Mathematics
Michigan State University
A-318 Wells Hall
East Lansing, MI 48824
United States
http://www.math.msu.edu/~redden