We know that: Torsion product Tor$^R_1(,)$, which maps two modules, $M_1$ over $R$ and $M_2$ over $R$, to a third module $M_3$ over $R$: $M_3$ = Tor$^R_1(M_1,M_2)$. See for examp …

I am asking this in the context of differential geometry (specifically Riemannian). When the Levi-Civita Connection is defined, we require that the torsion tensor is 0, which in l …

Thought Experiment Consider a 2-sphere, $S^2$, and let $p$ be a point at the equator. Case 1 Let us parallel transport a vector, $V$ from $p$ using the recipe: Move one unit o …

Hi, given a connection on the tangent space of a manifold, one can define its torsion: $$T(X,Y):=\triangledown_X Y - \triangledown_Y X - [X,Y]$$ What is the geometric picture behin …

Dear all, When dealing with General Relativity one uses the Levi-Civita connection with is torsion-free. Thus the commutator of the covariant derivatives yields $[\nabla_\mu,\nab …

This is, in a sense, a follow up to this question. Hehl and Obukhov try to give an intuitive description of torsion. I am confused about their description. I am looking at the fol …

Does there exist an integral domain $R$ and an $R$-module $M$ that is not flat over $R$ such that every tensor power of $M$ over $R$ is nonzero and $R$-torsion-free? (If such a do …

I'm interested in understanding the probability that given a prime $p$, $p$ divides the order of the torsional part of $H^k(X,Z)$, where $X$ is a finite simplicial complex. Lets s …