P. Buser and P. Sarnak showed in 1994 that the maximum, over the moduli space of Riemann surfaces of genus s, of the least conformal length of a nonseparating loop, is logarithmic in s. We present an application of (polynomially) dense Euclidean packings, to estimates for an analogous 2-dimensional conformal systolic invariant of a 4-manifold X with indefinite intersection form. The estimate tu...

We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts.

REMARK . The requirement that / be an odd prime can be dropped if K is totally imaginary. The groups on the right of (1.1) are continuous /-adic étale cohomology groups. Recall that Z//(l) denotes the sheaf of ^th roots of unity, Z/P(i) = (Z//(l))®, and Z,(0 = Hmv Z/l (i). D. Quillen has conjectured the existence of isomorphisms of type (1.1). B. Harris and G. Segal [4] have shown that (1.1) is...

Let G be a compact connected Lie group, and (M,ω) a compact Hamiltonian Gspace with moment map μ. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the original manifold M , under certain technical conditions on μ. This result is a natural K-theoretic analogue of the Kirwan surjectivity theorem in symplectic geomet...