A closed 4-manifold (or, more generally, a finite PD4space) has a finitely dominated infinite regular covering space if and only if either its universal covering space is finitely dominated or it is finitely covered by the mapping torus of a self homotopy equivalence of a PD3-complex. A Poincaré duality space is a space X of the homotopy type of a cell complex which satisfies Poincaré duality w...

Background: Epilepsy is a brain disorder that changes the basin geometry of the oscillation of trajectories in the phase space. Nevertheless, recent studies on epilepsy often used the statistical characteristics of this space to diagnose epileptic seizures. Objectives: We evaluated changes caused by the seizures on the mentioned basin by focusing on phase space sorted by Poincaré sections. Ma...

A notion of Poincaré series was introduced in [1]. It was developed in [2] for a multi-index filtration corresponding to the sequence of blow-ups. The present paper suggests the way to generalize the notion of Poincaré series to the case of arbitrary locally free sheaf on the modification of complex plane C 2. This series is expressed through the topological invariants of the sheaf. For the she...

We show that the relativistic analogue of the two types of time translation in a non-relativistic history theory is the existence of two distinct Poincaré groups. The ‘internal’ Poincaré group is analogous to the one that arises in the standard canonical quantisation scheme; the ‘external’ Poincaré group is similar to the group that arises in a Lagrangian description of the standard theory. In ...

The classical Poincaré weak recurrence theorem states that for any probability space (Ω,S, P ), any P -measure preserving transformation T , and any A ∈ S, almost all points of A return to A. In the present paper the Poincaré theorem is proved when the σ-algebra S is replaced by any σ-complete MV-algebra. Keywords— Measure preserving transformation, Poincaré recurrence theorem, σ-complete MV-al...