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Elliptic cohomology is a particularly lovely concept with each geometric and arithmetic points. The previous is defined by the truth that the idea is a quotient of oriented cobordism localised away from 2, the latter by the truth that the coefficients coincide with a ring of modular varieties. The goal of the book is to assemble this cohomology principle, and consider it on classifying areas BG of finite teams G. This class of areas is essential, since (utilizing concepts borrowed from `Monstrous Moonshine') it is feasible to offer a bundle-theoretic definition of EU-(BG). Concluding chapters additionally talk about variants, generalisations and potential purposes.
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