The Library
Infinite dimensional degree theory and Ramer's finite co-dimensional differential forms
Tools
Elworthy, K. David (2021) Infinite dimensional degree theory and Ramer's finite co-dimensional differential forms. Quarterly Journal of Mathematics, 72 (1-2). pp. 571-602. doi:10.1093/qmath/haab022 ISSN 0033-5606.
|
PDF
WRAP-Infinite-dimensional-degree-theory-Ramers-finite-differential-forms-2021.pdf - Accepted Version - Requires a PDF viewer. Download (934Kb) | Preview |
Official URL: http://dx.doi.org/10.1093/qmath/haab022
Abstract
Infinite-dimensional degree theory, especially for Fredholm maps with positive index as developed with Tromba, is combined with Ramer’s unpublished thesis work on finite co-dimensional differential forms. As an illustrative example, the approach of Nicolaescu and Savale to the Gauss–Bonnet–Chern theorem for vector bundles is reworked in this framework. Other examples mentioned are Kokarev and Kuksin’s approach to periodic differential equations and to forced harmonic maps. A discussion about how such forms and their constructions and cohomology relate to constructions for diffusion measures on path and loop spaces is also included.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Dimension theory (Topology), Differential forms, Gaussian measures, Infinite-dimensional manifolds | ||||||||
Journal or Publication Title: | Quarterly Journal of Mathematics | ||||||||
Publisher: | Oxford University Press | ||||||||
ISSN: | 0033-5606 | ||||||||
Official Date: | June 2021 | ||||||||
Dates: |
|
||||||||
Volume: | 72 | ||||||||
Number: | 1-2 | ||||||||
Page Range: | pp. 571-602 | ||||||||
DOI: | 10.1093/qmath/haab022 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The version of record K D Elworthy, Infinite-dimensional degree Theory And Ramer’s Finite Co-dimensional Differential Forms, The Quarterly Journal of Mathematics, 2021;, haab022, is available online at: https://doi.org/10.1093/qmath/haab022 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 26 April 2021 | ||||||||
Date of first compliant Open Access: | 23 April 2022 | ||||||||
Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year