EPSRC Reference: |
EP/H021566/1 |
Title: |
Symplectically oriented cohomology theories of algebraic varieties |
Principal Investigator: |
Garkusha, Professor G |
Other Investigators: |
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Researcher Co-Investigators: |
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Project Partners: |
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Department: |
College of Science |
Organisation: |
Swansea University |
Scheme: |
Standard Research |
Starts: |
27 April 2010 |
Ends: |
26 July 2010 |
Value (£): |
15,175
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EPSRC Research Topic Classifications: |
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EPSRC Industrial Sector Classifications: |
No relevance to Underpinning Sectors |
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Related Grants: |
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Panel History: |
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Summary on Grant Application Form |
The versatility of A^1-homotopy theory and its associated range of cohomological techniques has made it an important branch of mathematics. Recently there have been several fundamental developments which have been used to solve a number of longstanding problems. The new strategically important developments are related to the names of V. Voevodsky (Fields Medal 2002), M. Rost, A. Suslin, I. Panin, M.Levine, F. Morel.The principal aim of this proposal is the study of symplectically oriented cohomology theories on algebraic varieties introduced recently by Nenashev-Panin-Walter. We plan to construct bijective correspondences between symplectic orientations, Pontriagin structures, Pontriagin-Thom structures and symplectic trace structures (symplectic integrations) respectively on a given ring cohomology theory. Another aim of the project is to give an explicitdescription for symplectic trace structures on a symplectically oriented cohomology theory. The theory is illustrated by the symplectic algebraic cobordism of Voevodsky, the hermitian algebraic K-theory and by other examples.The research will be undertaken in the Department of Mathematics, Swansea University.
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Key Findings |
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Potential use in non-academic contexts |
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Impacts |
Description |
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Summary |
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Date Materialised |
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Sectors submitted by the Researcher |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Project URL: |
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Further Information: |
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Organisation Website: |
http://www.swan.ac.uk |