We extend knot contact homology to a theory over the ring Z[λ±1, μ±1], with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in S and can be generalized to knots in arbitrary manifolds, distinguishes the unknot and can distinguish mutants. It contains the Alexander polynomial and naturally produces a two-variable polynomial knot in...

Let X be a hypergroup. In this paper, we define a locally convex topology β on L(X) such that (L(X), β) with the strong topology can be identified with a Banach subspace of L(X). We prove that if X has a Haar measure, then the dual to this subspace is LC(X) ∗∗ = cl{F ∈ L(X);F has compact carrier}. Moreover, we study the operators on L(X) and L 0 (X) which commute with translations and convoluti...

We show that topologically expansive Lorenz maps can be described up to topological conjugacy by their kneading invariants. We also give a simple condition on pairs of symbol sequences which is satisfied if and only if that pair of sequences is the kneading invariant for some topologically expansive Lorenz map. A simple extension of the theorems to the case of expansive maps of the interval wit...

In this paper, we introduce and characterize the dynamically deened recurrence dimension, a new topological invariant number, following the idea of a previous article 9], but with some modiications and improvements. We study some example of Toeplitz subshifts for which we can show that the recurrence dimension is a topologically invariant number diierent from the topological entropy.

We show that the one-sided Dyck shift has a unique tail invariant topologically σ-finite measure (up to scaling). This invariant measure of the one sided Dyck turns out to be a shift-invariant probability. Furthermore, it is one of the two ergodic probabilities obtaining maximal entropy. For the two sided Dyck shift we show that there are exactly three ergodic double-tail invariant probabilitie...

Monopoles are expected to play an important role in confining quarks in QCD. In lattice simulations, one usually looks for U(1) monopoles by fixing an Abelian gauge [1]. However it is important to have a gauge invariant way of detecting monopoles in non-Abelian gauge theories. In a recent paper [2] Anishetty, Majumdar and Sharatchandra have given a criterion for characterizing topologically non...