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Elliptic cohomology. (English) Zbl 0946.55004

Cappell, Sylvain (ed.) et al., Surveys on surgery theory. Vol. 1: Papers dedicated to C. T. C. Wall on the occasion to his 60th birthday. Princeton, NJ: Princeton University Press. Ann. Math. Stud. 145, 409-439 (2000).
This paper is a survey of the current research using elliptic cohomology and its variants. The topics covered include the Witten genus and its relation to Ricci curvature, the relation to representation theory, and the role of the Mathieu groups in defining elliptic genera.
For the entire collection see [Zbl 0933.00057].

MSC:

55N34 Elliptic cohomology
55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology
55N35 Other homology theories in algebraic topology
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
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