What Are Stratified Manifolds and Their Role in Theoretical Physics?

[MathematicalPhysicist]

hi, i encountered this term in julian barbour webpage and i will like it if someone can tell me more about them?

 

[meteor]

Is a differentiable 2-manifold with singularities that are also differentiable manifolds themselves

Perhaps there's some relationship with the objects known as stratified vector bundles? Sorry, I'm not an expert

 

[jeff]

hi, i encountered this term in julian barbour webpage and i will like it if someone can tell me more about them?

I couldn't find this term on barbour's site or by googling. But knowing what he works on, by a "stratified" space he may have meant what is more commonly referred to as a "foliated" space, which roughly speaking is a space that has been expressed as a union of disjoint hypersurfaces, very much like a salami as a union of slices. In the context of the physics of spacetime, these hypersurfaces represent surfaces of simulteneity, with different observer's seeing the universe as being sliced up - foliated - in different ways. If this turns out not to be what he meant by "stratified", never mind.

 

[pelastration]

I couldn't find this term on barbour's site or by googling.

http://www.qgravity.org/discussion/jb/

quote:"Second, the approach based on a 3D continuum and factoring out symmetries (which leads to consideration of stratified manifolds) really does seem to me to lead to a deep insight into the structure of relativity and gauge theory. "

I like stratified spacetime.

 

[arivero]

On other hand, the (Fulton-MacPherson) stratification of configuration space is a very abstruse way to codify differential structure.

 

[MathematicalPhysicist]

I couldn't find this term on barbour's site or by googling. But knowing what he works on, by a "stratified" space he may have meant what is more commonly referred to as a "foliated" space, which roughly speaking is a space that has been expressed as a union of disjoint hypersurfaces, very much like a salami as a union of slices. In the context of the physics of spacetime, these hypersurfaces represent surfaces of simulteneity, with different observer's seeing the universe as being sliced up - foliated - in different ways. If this turns out not to be what he meant by "stratified", never mind.

well let's see if we are speaking about the same page.
i was referring to this website:
www.platonia.com in the link of ideas.

it was briefly described (i think this website is more promoting his book than provide explanations about his ideas).

 

[arivero]

http://www.platonia.com/ideas.html

I also plan to post on this website a paper explaining the rather brief remarks on p. 344 of my The End of Time about stratified manifolds, which are models of my central notion of Platonia (as explained in that book). Stratified manifolds occur widely in theoretical physics, and a question that has long interested me is the effect, if any, that the strata of these manifolds exert on classical dynamical trajectories and quantum wave functions defined on such manifolds.