| EPSRC Reference: |
GR/R84276/01 |
| Title: |
Methods of noncommutative algebra and deformation of structures in algebrraic topology |
| Principal Investigator: |
Lazarev, Professor A |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Fast Stream |
| Starts: |
21 October 2002 |
Ends: |
20 October 2005 |
Value (£): |
61,773
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The area of the proposed research in pure mathematics is stable homotopy theory and certain aspects of related algebra such as the theory of formal groups and deformation theory. Homotopy theory studies the properties of topological spaces which do not change under continuous deformations.The principal aim of this project is two-fold. First, we intend to investigate the global properties of the stable homotopy category such as the Taylor tower on the identity functor on S-algebras, Morita duality and moduli spaces of algebra structures. It is hoped that study of such phenomena will shed light on some classical problems in stable homotopy theory. Second, we propose to use methods and ideas from algebraic topology to study algebraic structures such as strongly homotopy associative algebras and formal groups. Particular attention will be paid to structures arising in the theory of complex cobordisms, one of the central objects of study in modern topology. The homotopy-theoretic outlook that we develop is likely to be useful in other areas of mathematics such as algebraic deformation theory and noncommutative geometry.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.bris.ac.uk |