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紀要論文

紀要論文

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Osaka Journal of Mathematics.51(1) P.89-P.119

WEIGHTED PROJECTIVE SPACES AND ITERATED THOM SPACES

Osaka University and Osaka City University, Departments of Mathematics

英語

2014-01

http://hdl.handle.net/11094/29185

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.

info:doi/10.18910/29185

WEIGHTED PROJECTIVE SPACES AND ITERATED THOM SPACES

Osaka University and Osaka City University, Departments of Mathematics

英語

2014-01

Osaka Journal of Mathematics

51

1

89

119

00306126

http://hdl.handle.net/11094/29185

info:doi/10.18910/29185