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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.
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
$D_{ij}$you want to type
D_{i j}
to produce
$D_{i j} \,.$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?
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
first item
second item
third item
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