In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space of dimension higher than two, which generalizes the notion of analytic finiteness in dimension two. Then we extend the argument in the paper of Bishop and Jones to show that conformal finiteness implies geometric fini...

The notion of the Cousin complex of a module was given by Sharp in 1969. It wasn’t known whether its cohomologies are finitely generated until recently. In 2001, Dibaei and Tousi showed that the Cousin cohomologies of a finitely generated A-module M are finitely generated if the base ring A is local, has a dualizing complex, M satisfies Serre’s (S2)-condition and is equidimensional. In the pres...

Abstract We prove the finiteness of formal analogs spherical function (Spherical Finiteness), ${\textbf c}$-function (Gindikin–Karpelevich and obtain a analog Harish-Chandra’s limit (Approximation Theorem) relating in setting $p$-adic Kac–Moody groups. The theorems imply that Gindikin–Karpelevich integral is well defined local settings. These results extend Braverman–Garland–Kazhdan–Patnaik’s a...

Consider a ring K, a topological space X and a sheaf A on X of K[[~]]-algebras. Assuming that A is ~-complete and without ~torsion, we first show how to deduce a coherency theorem for complexes of A -modules from a corresponding property for complexes of A /~A -modules. We apply this result to prove that, under a natural properness condition, the convolution of two coherent kernels over deforma...

Torelli space Tg (g ≥ 2) is the quotient of Teichmüller space by the Torelli group Tg. It is the moduli space of compact, smooth genus g curves C together with a symplectic basis of H1(C;Z) and is a model of the classifying space of Tg. Mess, in his thesis [12], proved that T2 has the homotopy type of a bouquet of a countable number of circles. Johnson and Millson (cf. [12]) pointed out that a ...

By imposing on the most general renormalizable quantum field theory the requirement of the absence of ultraviolet-divergent renormalizations of the physical parameters (masses and coupling constants) of the theory, finite quantum field theories in four space-time dimensions may be constructed. Famous “prototypes” of these form certain well-known classes of supersymmetric finite quantum field th...

We establish the ultraviolet finiteness of various classes of noncommutative gauge theories.