Perfect forms, K-theory and the cohomology of modular groups
نویسندگان
چکیده
For N = 5, 6 and 7, using the classification of perfect quadratic forms, we compute the homology of the Voronoï cell complexes attached to the modular groups SLN(Z) and GLN(Z). From this we deduce the rational cohomology of those groups and some information about Km(Z), when m = 5, 6 and 7.
منابع مشابه
Perfect Forms and the Cohomology of Modular Groups
For N = 5, 6 and 7, using the classification of perfect quadratic forms, we compute the homology of the Voronoï cell complexes attached to the modular groups SLN(Z) and GLN(Z). From this we deduce the rational cohomology of those groups.
متن کاملOperations and Cooperations in Elliptic Cohomology, Part I: Generalized modular forms and the cooperation algebra
This is the first of two interconnected parts: Part I contains the geometric theory of generalized modular forms and their connections with the cooperation algebra for elliptic cohomology, E``∗E``, while Part II is devoted to the more algebraic theory associated with Hecke algebras and stable operations in elliptic cohomology. We investigate the structure of the stable operation algebra E``∗E``...
متن کاملTopological modular forms with level structure
The cohomology theory known as Tmf, for “topological modular forms,” is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them. Along the way, we produce a natural way to re...
متن کاملAutomorphic Forms
We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n−1). These cohomology theories of topological automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...
متن کاملTopological Automorphic Forms
We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n−1). These cohomology theories of topological automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...
متن کامل