A comparison between cohomology and \(K\)-theory of weighted projective spaces
type: Item
instance of: scholarly article
title: A comparison between cohomology and \(K\)-theory of weighted projective spaces
zbMATH Open document ID: 0808.55005
DOI: 10.1016/0022-4049(94)90107-4
author: Abdallah Al Amrani
published in: Journal of Pure and Applied Algebra
publication date: 1995-03-16T00:00:00Z
review text: In [ibid., 113-127 (1994; see the review above)] the author computed the complex \(K\)-theory ring of \(P^ n_ \mathbb{C} (q_ 0,\dots, q_ n)\), the weighted projective space which is the quotient of \(\mathbb{C}^{n + 1} - \{0\}\) by the \(\mathbb{C}^*\)-action given by \(\lambda (\tau_ 0, \dots, \tau_ n) = (\lambda^{q_ 0} \tau_ 0, \dots, \lambda^{q_ n} \tau_ n)\). In this sequel he gives another calculation, which works only under restrictions on the \(\{q_ i\}\). The method, when it works, shows that \(K^*(P^ n_{\mathbb{C}} (q_ 0, \dots, q_ n))\) is isomorphic to the cohomology ring.
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 579991
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90107-4
OpenAlex ID: W2035705788
cites work: Complex \(K\)-theory of weighted projective spaces
description: scientific article; zbMATH DE number 579991