Elliptic Curves and Algebraic Topology
نویسنده
چکیده
Elliptic curves enter algebraic topology through “Elliptic cohomology”–really a family of cohomology theories–and their associated “elliptic genera”. • Arithmetic aspect: Modularity of elliptic genera, The spectrum TMF of “topological modular forms” and the calculation of π∗TMF →MF (Z), Hopkins’s proof of Borcherds’ congruences. • Physical aspect: Witten’s approach to elliptic genera via string theory. • Homotopy theoretic aspect: Relationship to chromatic program, Hopkins and Mahowald’s calculation of π∗S → π∗TMF .
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