Where can I find explicit formulas for the higher homotopies, which exhibit the cup product (in singular simplicial cohomology, say) as homotopy commutative on the cochain level? Same question in Cech cohomology.
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
|
11
5
|
|
|
|
|
8
|
Such homotopies are given by the $\smile_i$-products. Steenrod gives explicit formulas, IIRC, in [Steenrod, N. E. Products of cocycles and extensions of mappings. Ann. of Math. (2) 48, (1947). 290--320. MR0022071], but the easiest is to prove they exist using acyclic models. (Maybe Steenrod only deals with $\mathbb Z_2$ coefficients? I don't have access to the paper now :( ) |
||||||||||||||||
|
You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.
|
8
|
These operations in the singular setting were fully and explicitly developed and generalized beautifully by McClure and Smith (who also credit Benson and Milgram) in their paper "Multivariable cochain operations and little $n$-cubes": http://arxiv.org/pdf/math.QA/0106024.pdf |
|||
|
|
