Resolutions and periodicity

Periodicity and Almost-periodicity

Poincaré Duality and Periodicity, Ii. James Periodicity

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension ΣK so that the resulting space satisfies Poincaré duality. When this is possible, we say that ΣK is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then ΣK is a spine whenever j is a suitable power of two. The ...

Path categories and resolutions

The path category P (X) of a simplicial set X defines a functor X 7→ P (X) which is left adjoint to the nerve functor B : cat → sSet. The first section of this paper contains an elementary description of this functor, with some of its basic properties. This construction specializes to a path category functor for cubical sets which appears in the second section. The path category construction is...

SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

Periodicity and Quasi-periodicity for Super-integrable Hamiltonian Systems

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single-valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a com-mensurability condition is imposed on an angular momentum component. R ´ ESUMÉ...