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Mar
28
awarded  Guru
Mar
22
comment Refining homotopy commutative maps of spectra to maps of E_{\infty}-ring spectra
math.uiuc.edu/~mando/papers/koandtmf.pdf
Feb
11
comment What are necessary and sufficient conditions for the product of spheres to be paralellizable?
This is false for $S^{2n} \times S^{2n}$ with $n>0$, because the Euler class of the tangent bundle is nonzero.
Dec
31
awarded  Enlightened
Dec
31
awarded  Nice Answer
Dec
9
comment Orientable Surface Covers Non-Orientable Surface
I don't know what you're allowed to use but a nice fact about the Euler characteristic is that if $E \rightarrow B$ is an $n$-sheeted covering, then the Euler characteristic of $E$ is $n$ times the Euler characteristic of $B$. If $E$ is orientable, the Euler characteristic also equals $2-2g$, if it's non-orientable the Euler characteristic is $2-g$ where $g$ is the genus. So... consider the double cover. :)
Nov
21
awarded  algebraic-topology
Aug
17
comment Inclusion $O(2n)/U(n)\to GL(2n,\mathbb{R})/GL(n,\mathbb{C}) $
math.washington.edu/~mitchell/Notes/prin.pdf
Aug
17
comment Why is there no compact manifold without boundary with the following homology groups?
haha thanks Georges :)
Aug
16
comment How to give the coproduct of differential graded algebras explicitly?
What's the differential on $H_*(\Omega X)$?
Aug
16
answered Inclusion $O(2n)/U(n)\to GL(2n,\mathbb{R})/GL(n,\mathbb{C}) $
Aug
16
answered Why is there no compact manifold without boundary with the following homology groups?
Aug
9
comment Homotopy operator for the Gysin sequnce
What does "homotopy operator" mean?
Jul
29
comment Cohomology of the pullback of a fiber bundle over the torus (generalised Eilenberg-Moore spectral sequence?)
There is an Eilenberg-Moore spectral sequence for general connected base spaces; the trouble is that it doesn't always converge to thing you want unless the action of $\pi_1$ satisfies some nilpotent conditions. I can only find a reference for the case of a fibration, but the case of a homotopy pullback shouldn't be too different: www3.nd.edu/~wgd/Dvi/StrongConvergenceEilenbergMoore.pdf
Jul
29
awarded  Yearling
Jul
26
answered Is there a definition of the transfer homomorphism (between cohomology of cover and base) without referring to chains?
Jul
19
comment Loop space and $K$-theory
@ArthurStuart Forse stai pensando al "Bott map"? Vedi la prima risposta: mathoverflow.net/questions/8800/proofs-of-bott-periodicity
Jul
19
comment Homology of Compact Manifolds
The proof is not so bad, here is an outline: Every cpct manifold $X$ embeds into euclidean space (take an open cover $U_i$ and extend each map $U_i \subset \mathbb{R}^{n_i}$ to a map $X \rightarrow S^{n_i}$. Together we get an embedding into a product of spheres, which lives in Euclidean space). One checks that $X\subset \mathbb{R}^N$ is the retract of some open set $U$. Since $X$ is cpct, $X$ is inside some large simplex. Subdivide so that simplices lie entirely in $U$ or $U^c$ and restrict the retraction to those in $U$. Retracts of finite complexes have fg homology, so we're done.
Jul
19
comment Local homeomorphisms which are not covering map?
I see a similar example was used in the post linked in a comment... You can get lots of examples of this type by restricting covering maps. Another would be to restrict the cover $S^2 \rightarrow \mathbb{R}P^2$ to a little thickening of the upper hemisphere.
Jul
19
answered Local homeomorphisms which are not covering map?