called the cyclotomic character. It is even an isomorphism if K is linearly disjoint from Q(ζm). But that’s not class field theory, or rather it’s only a tiny part of class field theory for the field K. The proper, and much more stunning generalisation is a reciprocity isomorphism H ∼ −→ Gal(K(m)/K) between so called ray class groups H of modulus m and Galois groups of corresponding finite abel...

Let T be a compact torus and (M,ω) a Hamiltonian T -space. In a previous paper, the authors showed that the T -equivariant K-theory of the manifold M surjects onto the ordinary integral K-theory of the symplectic quotient M//T , under certain technical conditions on the moment map. In this paper, we use equivariant Morse theory to give a method for computing theK-theory of M//T by obtaining an ...

The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a ten-manifold X contains subtle phase factors that are associated with T-duality, self-duality, and the relation of the RR fields to K-theory. The analogous partition function of M-theory on X × S 1 contains subtle phases that are similarly associated with E 8 gauge theory. We analyze the detailed phase factors o...

SU(N) Yang-Mills theory in three dimensions, with a Chern-Simons term of level k (an integer) added, has two dimensionful coupling constants, gk and gN ; its possible phases depend on the size of k relative to N . For k ≫ N , this theory approaches topological Chern-Simons theory with no Yang-Mills term, and expectation values of multiple Wilson loops yield Jones polynomials, as Witten has show...

The now-famous Majumdar-Papapetrou exact solution of the EinsteinMaxwell equations describes, in general, N static, maximally charged black holes balanced under mutual gravitational and electrostatic interaction. When N = 2, this solution defines the two-black-hole spacetime, and the relativistic two-center problem is the problem of geodesic motion on this static background. Contopoulos and a n...