Skip to main content
MathOverflow

Return to Answer

added 1 characters in body
Source Link
Tim Porter
Tim Porter
  • 9.6k
  • 1
  • 27
  • 41

I wrote that part of the nLab entry so can confirm that it is the Edwards and Hastings extension of Chapman's result that was referred to, but my feeling in this is that that result is the geometric form of a lot of the classical cohomological duality results and that there should be more to be said about this ... but I don't know what! Perhaps looking at the Chapman result in the light of modern homotopy theory (say using Lurie's notion of shape) may give an $(\infty,1)$-categorical result. (Note that Batanin did work on strong shape theory and produced an $A_\infty$-structure, which must relate to this. Now I like that set of ideas. Good luck if you try it!)

(You may spur me on to write more on that entry as it has got stalled... Alternatively anyone else is welcome to write more on strong shape, of course.... and to correct any miswording, typos that they find. :-))

I wrote that part of the nLab entry so can confirm that it is the Edwards and Hastings extension of Chapman's result that was referred to, but my feeling in this is that that result is the geometric form of a lot of the classical cohomological duality results and that there should be more to be said about this ... but I don't know what! Perhaps looking at the Chapman result in the light of modern homotopy theory (say using Lurie's notion of shape) may give an $(\infty,1)$-categorical result. (Note that Batanin did work on strong shape theory and produced an $A_\infty$-structure, which must relate to this. Now I like that set of ideas. Good luck if you try it!

(You may spur me on to write more on that entry as it has got stalled... Alternatively anyone else is welcome to write more on strong shape, of course.... and to correct any miswording, typos that they find. :-))

I wrote that part of the nLab entry so can confirm that it is the Edwards and Hastings extension of Chapman's result that was referred to, but my feeling in this is that that result is the geometric form of a lot of the classical cohomological duality results and that there should be more to be said about this ... but I don't know what! Perhaps looking at the Chapman result in the light of modern homotopy theory (say using Lurie's notion of shape) may give an $(\infty,1)$-categorical result. (Note that Batanin did work on strong shape theory and produced an $A_\infty$-structure, which must relate to this. Now I like that set of ideas. Good luck if you try it!)

(You may spur me on to write more on that entry as it has got stalled... Alternatively anyone else is welcome to write more on strong shape, of course.... and to correct any miswording, typos that they find. :-))

Source Link
Tim Porter
Tim Porter
  • 9.6k
  • 1
  • 27
  • 41

I wrote that part of the nLab entry so can confirm that it is the Edwards and Hastings extension of Chapman's result that was referred to, but my feeling in this is that that result is the geometric form of a lot of the classical cohomological duality results and that there should be more to be said about this ... but I don't know what! Perhaps looking at the Chapman result in the light of modern homotopy theory (say using Lurie's notion of shape) may give an $(\infty,1)$-categorical result. (Note that Batanin did work on strong shape theory and produced an $A_\infty$-structure, which must relate to this. Now I like that set of ideas. Good luck if you try it!

(You may spur me on to write more on that entry as it has got stalled... Alternatively anyone else is welcome to write more on strong shape, of course.... and to correct any miswording, typos that they find. :-))