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 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 sheaves 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).
  1. I created branched manifold -linked from orbifold- with a definition from ”expanding attractors” by Robert F. Williams (1974) quoted in wikipedia. This description is -as it stands- not precisely compatible to that given in Dusa McDuffs ”Groupoids, Branched Manifolds and Multisections” which I am rather interested in. So I plan to comment on this as a side note in the -yet to be written-article orbifold groupoid.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 2nd 2012

    Thanks!

    I have edited the entry a little further: I have made the table of contents appear and added hyperlinks.

    I have also added a brief Idea-section, but beware that I haven’t really thought about branched manifolds much.

    One pedantic but hopefully useful note on typesetting: instiki differs from genuine TeX in how it renders variable names. If you put no whitespace in between letters in math mode, then the whole consecutive string of symbols is rendered in MathRoman and hence does not appear as a sequence of variables.

    So instead of typing

    D_{ij}
    

    which produces

    D ij D_{ij}

    you want to type

    D_{i j}
    

    to produce

    D ij. D_{i j} \,.
  2. I am on getting some systematics on the notions of orbifold groupoid with the intention of giving a most general one (and thereby not to rule out some variation of orbifold present in the literature). Following some reference (groupoids, manifolds and multisections) in regard to branched orbifolds I encountered the notion of polyfold (described e.g. in polyfolds and a general Fredholm theory). These are apparently situated in some topos for functional analysis where the smooth structure is replaced by ”sc-smoothness” defined via a grading of nested subspaces. Does anyone know if this setup fits in Jacob Luries ”structured spaces”?

    Thanks for the typographical hint! Reading ”branched manifold” I saw that the enumeration with ”:” inside the theorem-like environment does not work properly; is this a permanent feature?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 3rd 2012

    I saw that the enumeration with ”:” inside the theorem-like environment does not work properly; is this a permanent feature?

    I don’t know about this colon syntax. What I know how to make enumerate lists is via

    1. first item
    
    1. second item
    
    1. third item
    

    etc, which produces

    1. first item

    2. second item

    3. third item