We study some topological properties of maximal ideal spaces of certain algebras of almost periodic functions. Our main result is that such spaces are contractible. We present several analytic corollaries of this result. MSC: 42A75; 46J10

We reprove and generalize in a combinatorial way the result of A. Björner, [Bj81, Theorem 3.3], that order complexes of noncomplemented lattices are contractible, namely by showing that these simplicial complexes are in fact nonevasive, in particular collapsible.

The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical manifold carry contractible periodic orbits of the Hamiltonian flow, provided that the function attains its minimum along a closed symplectic submanifold. As...

We study a model of densely packed self-avoiding loops on the annulus, related to the Temperley Lieb algebra with an extra idempotent boundary generator. Four different weights are given to the loops, depending on their homotopy class and whether they touch the outer rim of the annulus. When the weight of a contractible bulk loop x ≡ q + q ∈ (−2, 2], this model is conformally invariant for any ...

Abstract Real Bruhat cells give an important and well-studied stratification of such spaces as $\operatorname {GL}_{n+1}$, {Flag}_{n+1} = \operatorname {SL}_{n+1}/B$, {SO}_{n+1}$, {Spin}_{n+1}$. We study the intersections a top dimensional cell with another (for basis). Such intersection is naturally identified subset lower nilpotent group {Lo}_{n+1}^{1}$. are particularly interested in homotop...