Thomas, Charles B. 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]. Reviewer: R.E.Stong (Charlottesville) Cited in 1 Document 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 Keywords:Witten genus; Ricci curvature; representation theory; Mathieu groups; elliptic genera PDFBibTeX XMLCite \textit{C. B. Thomas}, Ann. Math. Stud. 145, 409--439 (2000; Zbl 0946.55004)