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Jul
22
answered Refining homotopy commutative maps of spectra to maps of E_{\infty}-ring spectra
Mar
11
comment A group-like topological monoid is a loop space
Opps, I have no idea how that happened. I think I meant to link to this: math.stanford.edu/~carym/bar.pdf
Mar
11
comment A group-like topological monoid is a loop space
This probably depends on your model for $BM$, but see, for example, math.stackexchange.com/questions/704397/…
Feb
27
awarded  Yearling
Feb
19
comment A question about the universal coefficient theorem.
I think if you're careful about it, you'll find that the maps can be chosen to be $R$-module maps, but that the splitting is not one of $R$-modules
Jan
31
comment Universal Coefficient Theorem - what kind of morphisms?
But here you know what the map $H_n(X) \otimes \mathbb{Q} \to H_n(X;\mathbb{Q})$ is - and you know (on the chain level) where the module structure is coming from
Jan
30
comment Universal Coefficient Theorem - what kind of morphisms?
The point is that $H_1(X;\mathbb{Q})\simeq H_1(X) \otimes \mathbb{Q}$ both as abelian groups and as a $\mathbb{Q}$-vector space
Jan
30
comment Universal Coefficient Theorem - what kind of morphisms?
As an example, what can you say about $H_1(X;\mathbb{Q})$ as an abelian group, and as a vector space?
Jan
27
comment Cup Product Structure on the n-Torus
See the bottom of pp. 242: math.cornell.edu/~hatcher/AT/ATcapprod.pdf
Nov
19
comment If the connected sum of a manifold $M$ with itself gives back $M$, does it imply $M$ is a sphere?
@JasonDeVito: Oh, I totally misread the question! Hmm, now I'd like to see it as well
Nov
17
comment If the connected sum of a manifold $M$ with itself gives back $M$, does it imply $M$ is a sphere?
The swindle argument can be found here: terrytao.wordpress.com/2009/10/05/mazurs-swindle.
Oct
11
comment Spaces such that $\Omega^2 X \cong X$
$\Omega^2 U = U$ (which corresponds to complex $K$-theory in Piotr's answer)
Sep
25
comment Creating connective spectra from infinite loop spaces
There is more said here: math.stackexchange.com/questions/81472/…
Sep
25
answered Creating connective spectra from infinite loop spaces
Sep
24
comment Fibre homotopy equivalence
Yes this is true. See pp. 52 math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
Sep
23
comment Using Mapping cone to show map induce isomorphism on homology
It is in disguise. Up to homotopy we can assume $f$ is a cofibration, and so we can identify $C(f)$ with $Y/X$, and then this is just the long exact sequence in (relative) homology along with an identification $\tilde H_n(Y,X) = \tilde H_n(Y/X)$
Sep
23
answered Using Mapping cone to show map induce isomorphism on homology
Sep
11
answered Identity in Thom spaces.
Aug
6
comment Cohomology ring of $U(n)$
If I understand the question and you are happy to use the Serre spectral sequence I think this comes out pretty easily from the sparseness of the spectral sequence.
Jul
22
comment There is more then one Homology Theory for spaces, which are not Hausdorff
You should be able to compare Cech (co)homology with singular: see mathoverflow.net/questions/1750/…