Hopkins, Michael J. Topological modular forms, the Witten genus, and the theorem of the cube. (English) Zbl 0848.55002 Chatterji, S. D. (ed.), Proceedings of the international congress of mathematicians, ICM ’94, August 3-11, 1994, Zürich, Switzerland. Vol. I. Basel: Birkhäuser. 554-565 (1995). This paper describes a formal framework in which to understand elliptic genera, orientations of highly parallelizable bundles in elliptic cohomology, and elliptic spectra. Much of the presentation is given in terms of abstract notions of elliptic curve. The most innovative aspect is the description of orientations and genera for the connective cover \(\text{BU} \langle 6 \rangle\) of BU. This is based on three complex line bundles and is called a cubical structure.For the entire collection see [Zbl 0829.00014]. Reviewer: R.E.Stong (Charlottesville) Cited in 6 ReviewsCited in 20 Documents MSC: 55N22 Bordism and cobordism theories and formal group laws in algebraic topology Keywords:elliptic genera; highly parallelizable bundles; elliptic cohomology; elliptic spectra PDFBibTeX XMLCite \textit{M. J. Hopkins}, in: Proceedings of the international congress of mathematicians, ICM '94, August 3-11, 1994, Zürich, Switzerland. Vol. I. Basel: Birkhäuser. 554--565 (1995; Zbl 0848.55002)