Equivariant homology decompositions for projective spaces and associated results/ Aparajita Karmakar

Thesis (Ph.D.)- Indian statistical Institute, 2023

Includes bibliography

Preliminaries on Equivariant Homotopy -- Equivariant cohomology with integer coefficients -- Homology Decompositions for Projective Spaces -- Homology decompositions for connected sums -- Ring Structure for Projective Spaces

Guided by Prof. Samik Basu

The purpose of this thesis is to discuss new calculations for the equivariant cohomology
of complex projective spaces. Given a complex representation V of a group G, one
obtains a “linear” G-action on P(V ) = the space of lines in V . The underlying space here is CPdim(V )−1 whose homology computation is well-known. The Borel-equivariant cohomology, which is the cohomology of the Borel construction, is easy to calculate as the space P(V ) has non-empty fixed points.