BAHRI, ANTHONY

FRANZ, MATTHIAS

RAY, NIGEL

For any weight vector χ of positive integers, the weighted projective space P(χ) is a projective toric variety, and has orbifold singularities in every case other than standard projective space. Our principal aim is to study the algebraic topology of P(χ), paying particular attention to its localisation at individual primes p. We identify certain p-primary weight vectors π for which P(π) is homeomorphic to an iterated Thom space, and discuss how any weighted projective space may be reassembled from its p-primary parts. The resulting Thom isomorphisms provide an alternative to Kawasaki's calculation of the cohomology ring of P(χ), and allow us to recover Al Amrani's extension to complex K-theory. Our methods generalise to arbitrary complex oriented cohomology algebras and their dual homology coalgebras, as we demonstrate for complex cobordism theory, the universal example. In particular, we describe a fundamental class that belongs to the complex bordism coalgebra of P(χ), and may be interpreted as a resolution of singularities

Bahri, Anthony

Franz, Matthias

Ray, Nigel

Osaka University Knowledge Archive

WEIGHTED PROJECTIVE SPACES AND ITERATED THOM SPACES

The University of Manchester - Institutional Repository

Weighted projective spaces and iterated Thom spaces

Osaka City University Repository

http://ir.library.osaka-u.ac.jp/dspace/bitstream/11094/29185/1/ojm51_01_089.pdf

Weighted projective spaces and iterated Thom spaces

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Osaka University Knowledge Archive

The University of Manchester - Institutional Repository

Osaka City University Repository