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)

 

Zeta forms and the local family index theorem


Author: Simon Scott
Journal: Trans. Amer. Math. Soc. 359 (2007), 1925-1957
MSC (2000): Primary 58J40, 58J52
Published electronically: December 19, 2006
MathSciNet review: 2276607
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a family $ F$ of elliptic pseudodifferential operators we show there is a natural zeta-form $ \zeta(F,S)$ and zeta-determinant form $ {det}_\zeta(F)$ in the ring of smooth differential forms on the parameterizing manifold, generalizing the classical single operator zeta-function and zeta-determinant. We show that the zeta forms extend the Atiyah-Bott-Seeley formula for the index of an elliptic operator to a family of elliptic operators, while the zeta-determinant form leads to a graded Chern class form for the index bundle. Globally, the zeta-form and zeta-determinant form exist only at the level of $ K$-theory as maps to cohomology.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 58J40, 58J52

Retrieve articles in all journals with MSC (2000): 58J40, 58J52


Additional Information

Simon Scott
Affiliation: Department of Mathematics, King’s College London, London, WC2R 2LS England
Email: simon.scott@kcl.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04321-2
PII: S 0002-9947(06)04321-2
Received by editor(s): May 4, 2004
Published electronically: December 19, 2006
Article copyright: © Copyright 2006 American Mathematical Society