Cencelj, Matija (1992) Localised equivariant cohomology and Milnor's additivity. PhD thesis, University of Warwick.

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Abstract

Borel equivariant cohomology, H τ (X:R), for spaces with circle action is a module over R[u], where u has degree 2. Localised equivariant cohomology u -1 H τ (X:R), provides certain information about H τ (X:R) but as a cohomology theory it has a deficiency in that it does not satisfy Milnor's additivity axiom.

In this thesis an equivariant cohomology theory, h τ, is constructed which agrees with u-1 H τ on nice finite-dimensional spaces with circle action and satisfies Milnor's additivity axiom. This has already been done by J.D.S. Jones and S.B. Petrack for the smooth case, where a different method was used which cannot be extended to the general case. We show that h τ satisfies a fixed point theorem similar to the one for u-1 H τ on finite dimensional spaces. Finally, cellular versions of H τ (X:Z), and u -1 H τ (X:Z), are constructed.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Homology theory, Cohomology operations
Official Date:	1992
Dates:	Date Event 1992 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Jones, J. D. S. (John D. S.)
Sponsors:	Research Council of Slovenia ; Iskra Holding ; Slovenia. Ministrstvo za znanost in tehnologijo
Extent:	87 leaves
Language:	eng

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