Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 4th 2011

    I have tried to make the page torsion look more like a disambiguation page and less like a mess. But only partially successful.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 5th 2011

    Heh. I wrote something at the Café, speculating where the term “flat” (as in “flat module”) came from. The wild speculation is that whoever invented the word wanted something that would sound sort like a synonym of “torsionfree” (which for modules over a PID coincides with “flat”), and by a kind of oblique free association, recalled that “torsionfree” for curves in 3\mathbb{R}^3 means “flat” (planar).

    No, I am not confused about the meanings of these terms! I know full well these are very different senses, and I’d have to ascribe a quirky sense of humor to any mathematician who would re-invent the term “flat” based on such a free association. It otherwise means little, and I’m sorry if Urs felt duty-bound to set the record straight (when he surely has more important things to think about).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 5th 2011

    Hey Todd,

    you write:

    I’m sorry if Urs felt duty-bound to set the record straight

    no need to apologize! It is true that your comment on the Café made me have a look at our nnLab entry on torsion, but it was not to set straight any record, just to bring that entry into better shape.

    I find your observation quite interesting. The relation of terms that you suggested had not occured to me before. I had thought that, like “torsion”, “flat” is a word that has been re-used for completely independent phenomena again and again. Witnessed for instance by the fact that even if you are indeed right and somebody really meant to refer to differential geometry when coining the word “flat module”, there is then a striking clash with the at least now most common use of “flat = no curvature”!