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Mar
29
comment SImple homotopy type of a mapping cone
What is the homology complex of a CW complex? What is simple homotopy equivalence for (presumably chain) complexes?
Mar
21
awarded  Nice Question
Mar
13
comment Reference: Relative cohomology of a morphism
As Denis says, relative (co)homology is widely used when talking of pairs given by a space and a(n appropriate) subspace, but it is commonly remarked in most books that if you have a map, you can do de same by taking the mapping cylinder, which turns it into an inclusion. Any book will do, e.g. Hatcher, Spanier, Switzer, Whitehead...
Mar
4
comment Semidirect product of semidirect products
I can think of some very trivial conditions which probably don't interest you. Probably if you say more about your situation you can get better answers.
Feb
24
comment Is there an obstruction which classifies “quasi-isomorphism but not chain equivalence”?
A nice reference dealing with this kind of problem in great generality is Weiss's "Hammock localization in Waldhausen categories", but your setting doesn't fit because the class of quasi-isomorphisms is not the saturation of the class homotopy equivalences. I would say that the answer is 'no' in your case, but don't expect a counterexample (at least from me). You can still define an obstruction in relative $K$-theory whose vanishing is necessary, but sufficiency seems to need Weiss hypotheses or something similar.
Feb
24
answered When does the projective model structure on functors exist?
Feb
24
comment coefficient of homology of configuration spaces over real projective spaces
Don't take my previous comment that literally. I was suggesting that you could ask him.
Feb
24
comment When does the projective model structure on functors exist?
I found it easily in Hirschhorn's book. It's in 11.6 Diagrams in a cofibrantly generated model category. The answer is always, provided $\mathcal K$ is cofibrantly generated (Theorem 11.6.1). For him (as well as for Hovey), the small object argument is (2), actually replacing cof with cell (Definitions 10.5.15 and 10.5.12).
Feb
24
comment coefficient of homology of configuration spaces over real projective spaces
I would ask him.
Feb
23
comment Spectral sequence of a bicomplex equipped with a group action
@SebastianGoette You're right, I somehow missed the track of the fact that we have a tensor product.
Feb
23
comment Spectral sequence of a bicomplex equipped with a group action
The answer is not positive in general, not even for $G$ finite. Take $G=\{1\}$. You can also construct more involved examples, of course.
Feb
23
comment When do you use “s” apostrophe to refer to authors ($e.g.$ of inequalities)?
I'd say you may find a better answer in english.stackexchange.com
Feb
22
reviewed Close Continuous inclusions Sobolev theorem, question
Feb
19
reviewed Close Ravi Vakil: Foundations of Algebraic Geometry, Exercise 18.4 J
Feb
19
comment $A_{\infty}$-structure on closed manifold
@IliasAmrani you should maybe stress that $\mathcal A$ is the unital associative operad (all spaces can be endowed with topological semigroup structures).
Feb
19
comment $A_{\infty}$-structure on closed manifold
Ilias, how do you make End(X) a reduced operad?
Feb
18
comment $A_{\infty}$-structure on closed manifold
@IliasAmrani as it's said in the first paragraph, examples are to be found in the paper by Hilton and Roitberg, which Vladimir links to in his answer.
Feb
18
answered $A_{\infty}$-structure on closed manifold
Feb
16
comment How to construct a free 2-group on a groupoid?
As you know, this passage from crossed modules to groupoids is equivalent to taking the loop space. The 'free object' Tom asks about is the 2-type of the suspension.
Feb
15
comment How to construct a free 2-group on a groupoid?
I mean crossed module of groups.