We study the arithmetic codings of hyperbolic automorphisms of the 2torus, i.e. the continuous mappings acting from a certain symbolic space of sequences with a finite alphabet endowed with an appropriate structure of additive group onto the torus which preserve this structure and turn the two-sided shift into a given automorphism of the torus. This group is uniquely defined by an automorphism,...

Let X be an irreducible smooth projective curve defined over complex numbers, S = {p1, p2, . . . , pn} ⊂ X a finite set of closed points and N ≥ 2 a fixed integer. For any pair (r, d) ∈ N × 1 N Z, there exists a parabolic vector bundle Rr,d,∗ on X , with parabolic structure over S and all parabolic weights in 1 N Z, that has the following property: Take any parabolic vector bundle E∗ of rank r ...

Suppose A is a C*-algebra and B is a Banach algebra such that it can be continuously imbedded in B(H), the Banach algebra of bounded linear operators on some Hubert space H. It is shown that if 6 is a compact algebra homomorphism from A into B, then 6 is a finite rank operator, and the range of 0 is spanned by a finite number of idempotents. If, moreover, B is commutative, then 9 has the form 8...

Homomorphism complexes were introduced by Lovász to study topological obstructions to graph colorings. We show that folding in the second parameter of the homomorphism complex yields a homotopy equivalence. We study how the Mycielski construction changes the homotopy type of the homomorphism complex. We construct graphs showing that the topological bound obtained by odd cycles can be arbitraril...

We say that two unitary or orthogonal representations of a finitely generated group G are additive conjugates if they intertwined by an map, which need not be continuous. associate to each representation topological action is complete conjugacy invariant: the automorphisms on Bohr compactification underlying Hilbert space. Using this construction we show property having almost invariant vectors...

In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.

where (x, g) denotes % evaluated at g. Each % thus yields a homomorphism of M(G) onto the complex numbers. Every such homomorphism of L(G) is obtained in this way. Let be a homomorphism of L{G) into M(H). After composing with <[>, every homomorphism of M(H) onto the complex numbers either is identically zero, or can be identified with a member of G. We thus have a map <£* from Ê into {G, 0 ...

The Nielsen Realization problem asks when the group homomorphism Diff(M) → π0Diff(M) admits a section. For M a closed surface, Kerckhoff proved that a section exists over any finite subgroup, but Morita proved that if the genus is large enough then no section exists over the entire mapping class group. We prove the first nonexistence theorem of this type in dimension 4: if M is a smooth closed ...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.