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For a topological dynamical system (X, f), consisting of a continuous map f : X → X, and a (not necessarily compact) set Z ⊂ X, Bowen [2] defined a dimension-like version of entropy,hX(f, Z). In...
Fractional Analytic Index     Fractional  Analytic Index       2015/3/19
Fractional Analytic Index.
Abstract: We calculate the equivariant index formula for an infinite dimensional Clifford module canonically associated to any Riemannian manifold. It encompasses the fractional index formula of the p...
Abstract: Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, we prove the local index formula for spectral triples over nonunital alg...
A conjecture of AutoGraphiX on the relation between the Randi´c index R and the algebraic connectivity a of a connected graph G is:R a  n − 3 + 2p2 2 ! /  2(1 − cos  n )  with ...
We give an algorithm for finding the index of a positive outer au-tomorphism of the free group, and prove the algorithm exits in a finite time.
Using generalized Cayley graphs and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index $1$.
Let $C^*(E)$ be the graph $C^*$-algebra associated to a graph E and let J be a gauge invariant ideal in $C^*(E)$. We compute the cyclic six-term exact sequence in $K$-theory of the associated extensio...
In this paper, we show that if p is a prime and G is a p-solvable group, then |G: Op(G)|p  (b(G)p/p)1/(p−1) where b(G) is the largest character degree of G. If p is an odd prime that is not a M...
A tangled diagram on [n] = {1,..., n} is a labeled graph for which each vertex has degree at most two. The vertices are arranged in increasing order on a horizontal line and the arcs are drawn in the ...
A tangled diagram on [n] = {1,..., n} is a labeled graph for which each vertex has degree at most two. The vertices are arranged in increasing order on a horizontal line and the arcs are drawn in the ...
In this paper we prove several theorems about the behavior of index of Lie algebras derived from associative algebras under tensor products of underlying associative algebras.
Cycloidal normal subgroups, that is, subgroups with only one cusp, of finite index of Hecke groups, which have been introduced by E. Hecke, and can be thought of as some kind of generalisation of the ...

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