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K(1)-local topological modular forms, the Witten orientation and E_\infty cellular structures

Thursday 12th December 2002 - 10:00 to 11:00
INI Seminar Room 1
Session Title: 
Elliptic cohomology and chromatic phenomena
We describe the construction and the orientation of the topological modular forms spectrum tmf in the K(1)-local E_\infty category at the prime 2. We use the theory of theta algebras to decompose tmf and the bordism theory MO into E_infty cells: MO splits into the cone T_\zeta and a free part. Moreover, as was shown by Mike Hopkins, the spectrum tmf is obtained from T_\zeta by attaching one more cell. With this information we give an explicit E_\infty orientation which refines the Witten genus for families of O manifolds.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons