All Questions
Tagged with noncommutative-geometry foliations
11 questions
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A foliation with prescribed graph of foliation
**I have already asked this question on MSE https://math.stackexchange.com/questions/4272279/1-dimensional-foliation-of-surfaces-with-prescribed-graph-of-foliation **
Definition of the graph of a ...
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A quantity associated to a foliated manifold and its non-commutative interpretation
Let $M$ be a compact $n$-dimensional manifold. Assume that $F$ is a $k$-dimensional foliation of $M$.
The graph $G(M,F)$ of this foliation is a $(n+k)$-dimensional manifold. We recall its definition:
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1
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Equivalence of two approaches to transverse measures for a foliation
Suppose that $(V,F)$ is a foliated manifold. There are three equivalent approaches to the notion of transverse measure as described in this book (see pages 65-69). I would like to understand the last ...
- 9,330
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C*-algebra of a singular surface foliation
Noncommutative geometry associates a $C^*$-algebra $C^*(S,{\cal F})$ with a foliation $\cal F$ on a manifold $S.$
Did somebody study this construction for noncompact surfaces $S$?
What I am really ...
- 2,390
3
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Causal fermion systems fromm fractal geometry
Okay, first off- I apologise if this is a stupid question. I'm mainly a very young physics guy, but this has primarily math basis. I'm trying to build a theory that is, long story short, some ...
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Foliations, von Neumann algebras and measurability
In the excellent book Noncommutative Geometry by Alain Connes much of the first chapter is devoted to foliations. At the end of the first chapter the author discusses index theory on measured ...
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69
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What is a foliation and why should I care?
The title says everything but while it is a little bit provocative let me elaborate a bit about my question. First time when I met the foliation it was just an isolated example in the differential ...
- 9,330
2
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A noncommutative vector bundle associated with a codimension one foliation
Assume that we have a codimension one foliation of a manifold $M$ which is generated by a one form $\alpha$. So the following $\phi$ satisfies $\phi \circ \phi =0$:$$\phi:\Omega^{i}(M)\to \...
- 356
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Product of two foliations
1.What is an example of a manifold $M$ with two foliations $F$ and $F'$ which are not topological equivalent but the product foliations $F\times F$ and $F'\times F'$, as foliations on $M\times M$, ...
- 356
12
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1
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"The" kronecker foliation or "a" kronecker foliation?
Consider the following two foliations of torus:
1)The Kronecker foliation with slope $\sqrt{2}$
2)The Kronecker foliation with slope $\pi$
As I learn from the literature, these two foliations are ...
- 356
9
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C*-algebras, foliations and dynamical systems
I am a Ph.D student involved in topics like integrability of foliations arising from center stable bundles of partially hyperbolic dynamical systems. These are generally only continuous bundles, so ...
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