Let ΩX be the space of Moore loops on a finite, qconnected, n-dimensional CW complex X , and let p be an odd prime. We prove the theorem: If p ≥ n/q, then the Hurewicz homomorphism induces isomorphisms U(Fπ∗(ΩX(p))) = −→ FH∗(ΩX(p)) and UE ∞ π (ΩX) = −→ E∞ H (ΩX) of Hopf algebras, where E ∞ π and E ∞ H are the limit terms of the homotopy and homology Bockstein spectral sequences, respectively, a...

We say that a countable discrete group Γ satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every Γ- subalgebra M in L(Γ) is of form L(Λ) for some normal subgroup Λ◁Γ. show many “negatively curved” groups, including all torsion free non-amenable hyperbolic groups and with positive first L2-Betti number under mild assumption, certain finite direct product them have this p...

Given a periodic quotient of torsion-free hyperbolic group, we provide fine lower estimate the growth function any sub-semi-group. This generalizes results Razborov and Safin for free groups.

we study algebraic properties of categories of merotopic, nearness, and filter algebras. we show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. the forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

It is well-entrenched folklore that torsion gravity theories predict observationally negligible torsion in the solar system, since torsion (if it exists) couples only to the intrinsic spin of elementary particles, not to rotational angular momentum. We argue that this assumption has a logical loophole which can and should be tested experimentally. We give an explicit counterexample where a rota...

In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a chain homotopy invariant on the collection of all quasi-isomorphisms from a bas...

Let k be an algebraically closed field of characteristic 0, and let A = k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M without free summands, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism ∇ : Derk(A) → Endk(M) that satisfy the derivation property and preserves the Lie product. In particular, a torsio...

In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a chain homotopy invariant on the collection of all quasi-isomorphisms from a bas...

The known facts about solvability of equations over groups are considered from a more general point of view. A generalized version of the theorem about solvability of unimodular equations over torsion-free groups is proved. In a special case, this generalized version become a multivariable variant of this theorem. For unimodular (ordinary and generalized) equations over torsion free groups, we ...

We will establish in this note a stability result for sparse convolutions on torsion-free additive (discrete) abelian groups. Sparse convolutions on torsion-free groups are free of cancellations and hence admit stability, i.e. injectivity with a universal lower bound α = α(s, f), only depending on the cardinality s and f of the supports of both input sequences. More precisely, we show that α de...