Timeline for What is a foliation and why should I care?
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 7, 2022 at 12:42 | comment | added | P. Grabowski | Foliations allow you to study families of manifolds such as fibrations, or orbits of Lie group actions, a geometry, by simpler objects sets of vector fields, an algebra, because from a family by a relative tangent bundle we get an inclusion from nice families into foliations. This is a significant reduction of complexity! | |
| Mar 28, 2021 at 17:47 | answer | added | Daniel Asimov | timeline score: 10 | |
| Mar 26, 2021 at 2:36 | comment | added | Mozibur Ullah | Fibre bundles are important in physics where they are used to describe gauge theories. It turns out that fibre bundles are very simple examples of foliations. So one perspective is that foliations generalise fibre bundles. For example, the holonomy groupoid of foliations generalise that of fibre bundles. | |
| Aug 16, 2020 at 13:15 | comment | added | Hollis Williams | If I remember rightly, there are some nice pictures of foliations in Lee's Introduction to Smooth Manifolds. | |
| Feb 7, 2016 at 16:48 | vote | accept | truebaran | ||
| Feb 7, 2016 at 15:11 | comment | added | user21349 | In general relativity you see foliations over and over as ways of discussing Cauchy problems and the time evolution of systems. These are foliations using spacelike surfaces. Because GR doesn't have a preferred time coordinate or a preferred notion of simultaneity, a foliation in spacelike surfaces is the next best thing. | |
| S Feb 7, 2016 at 9:32 | history | suggested | Ali Taghavi |
I change a tag
|
|
| Feb 7, 2016 at 9:30 | comment | added | Ali Taghavi | At the preface of this one read "The present monograph is an attempt to a better understanding of an interdisciplinary question, namely the impact of foliation theory on the geometry and analysis on CR manifolds", ams.org/books/surv/140/surv140-endmatter.pdf | |
| Feb 7, 2016 at 9:11 | comment | added | Ali Taghavi | This is a paper on NCG aspects of foliation sciencedirect.com/science/article/pii/0022123685900382 | |
| Feb 7, 2016 at 9:09 | comment | added | Ali Taghavi | @truebaran The holonomy groupoid of a foliation is used to associate a C* algebra to a foliation. This groupoid is based on the concept of holonomy of a leaf. The later is a generalization of the Poincare return map of a closed orbit of a vector field.BTW the NCG methods can be used to prove that the Kronecker foliation with slops $\alpha$ and $\beta$ are not topological equivalent if these slops are not in the same orbit of the action of $Sl(2,\mathbb{Z})$. | |
| Feb 7, 2016 at 8:58 | review | Suggested edits | |||
| S Feb 7, 2016 at 9:32 | |||||
| Feb 7, 2016 at 4:59 | comment | added | Trent | On a philosophical note, Connes motivates foliations as the simplest geometry of von neumann factorization and von neuman factorization as how time emerges. (Relevant excerpt from Connes' (english) Temps et Aléa du Quantique (youtube.com/watch?v=ODAngTW8deg) talk excerpted here: ncatlab.org/nlab/show/time). | |
| Feb 7, 2016 at 4:01 | answer | added | Pablo Lessa | timeline score: 95 | |
| Feb 7, 2016 at 3:28 | history | edited | Nik Weaver |
add a tag
|
|
| Feb 7, 2016 at 2:30 | answer | added | Pierre | timeline score: 21 | |
| S Feb 7, 2016 at 2:15 | history | suggested | Tadashi |
Added relevant tag
|
|
| Feb 7, 2016 at 2:08 | answer | added | Nik Weaver | timeline score: 22 | |
| Feb 7, 2016 at 1:54 | review | Suggested edits | |||
| S Feb 7, 2016 at 2:15 | |||||
| Feb 7, 2016 at 1:28 | review | Close votes | |||
| Feb 7, 2016 at 9:33 | |||||
| Feb 7, 2016 at 1:18 | comment | added | André Henriques | Leaf spaces of a foliations are examples of stacks, and there's no need to go to C*-algebras to talk about them. Now... you might what to ask another question: "What is a stack and why should I care?". ;-) | |
| Feb 7, 2016 at 0:44 | history | asked | truebaran | CC BY-SA 3.0 |