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

By: Material type: TextTextPublication details: Kolkata: Indian Statistical Institute, 2023Description: x, 90 pages; digSubject(s): DDC classification:
  • 23 514.23  Ap639
Online resources:
Contents:
Preliminaries on Equivariant Homotopy -- Equivariant cohomology with integer coefficients -- Homology Decompositions for Projective Spaces -- Homology decompositions for connected sums -- Ring Structure for Projective Spaces
Production credits:
  • Guided by Prof. Samik Basu
Dissertation note: Thesis (Ph.D.)- Indian statistical Institute, 2023 Summary: 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.
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Holdings
Item type Current library Call number Status Notes Date due Barcode Item holds
THESIS ISI Library, Kolkata 514.23 Ap639 (Browse shelf(Opens below)) Available E-thesis TH592
Total holds: 0

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.

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