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Integral generalized equivariant cohomologies of weighted Grassmann orbifolds

Koushik Brahma and Soumen Sarkar

Algebraic & Geometric Topology 24 (2024) 2209–2244
Abstract

We introduce a new definition of weighted Grassmann orbifolds. We study their several invariant q–CW complex structures and the orbifold singularities on the q–cells of these q–CW complexes. We discuss when the integral cohomology of a weighted Grassmann orbifold has no p–torsion. We compute the equivariant K–theory ring of weighted Grassmann orbifolds with rational coefficients. We introduce divisive weighted Grassmann orbifolds and show that they have invariant CW complex structures. We calculate the equivariant cohomology ring, equivariant K–theory ring and equivariant cobordism ring of a divisive weighted Grassmann orbifold with integer coefficients. We discuss how to compute the weighted structure constants for the integral equivariant cohomology ring of a divisive weighted Grassmann orbifold.

Keywords
weighted Grassmann orbifold, $q$–CW complex, divisive weighted Grassmann orbifold, equivariant cohomology ring, equivariant K-theory ring, equivariant cobordism ring, weighted structure constant.
Mathematical Subject Classification
Primary: 14M15, 19L47, 55N91, 57R18, 57R85
References
Publication
Received: 25 June 2022
Revised: 27 February 2023
Accepted: 10 April 2023
Published: 16 July 2024
Authors
Koushik Brahma
Department of Mathematics
Indian Institute of Technology Madras
Chennai
India
Soumen Sarkar
Department of Mathematics
Indian Institute of Technology Madras
Chennai
India

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