Contents

Idea

Topological automorphic forms are a generalization of topological modular forms: where the latter come with the moduli space of elliptic curves, topological automorphic forms are associated to a given Shimura variety. Moreover, just as topological modular forms refine to the tmf-spectrum representing the corresponding cohomology theory, so every Shimura variety induces a cohomology theory $taf$.

Properties

Chromatic pattern

chromatic level $n =$12$\geq 3$
cohomology theory/spectrum $E =$KOTMFTAF
algebraic group$GL_1$$GL_2$$U(1,n-1)$
geometric objectmultiplicative groupelliptic curveShimura variety
FQFTsuperparticleheterotic superstring??

References

The definition is due to

An introductory survey is in

Lecture notes include

Revised on May 18, 2014 07:56:48 by Urs Schreiber (82.113.121.154)