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answered Topological Derivation of Leray Spectral Sequence
Feb
8
comment What (fun) results in graph theory should undergraduates learn?
@post.as.a.guest: I would say that yes, fun is a principal criterion (although not the principal criterion). Students who are having fun are more likely to be inspired to learn.
Feb
3
awarded  Popular Question
Jan
29
comment Is every homology theory given by a spectrum?
I don't know, this might be a good MO question! An Exercise in Hatcher's 4.F is to show that the wedge axiom implies the direct limit axiom on the category of countable CW complexes, so to find such a thing we'd have to go to uncountable CW complexes.
Jan
24
comment A dictionary of Characteristic classes and obstructions
Regarding the Euler class, the "only if" statement is not true without some restrictions (such as the rank of the vector bundle equaling the dimension of the base). See here mathoverflow.net/questions/31376/vanishing-of-euler-class
Jan
19
comment Milnor's model of $EG$ and Kac-Moody groups
I added the at.algebraic topology tag as this might attract more people qualified to answer.
Jan
19
revised Milnor's model of $EG$ and Kac-Moody groups
edited tags
Jan
18
answered Book recommendation for cobordism theory
Jan
8
awarded  Popular Question
Jan
6
awarded  Enlightened
Jan
6
awarded  Nice Answer
Jan
2
comment torsion part of the cohomology module of configuration spaces of manifolds
The paper shows there is no $p$-torsion for $p\ge3$.
Dec
31
answered torsion part of the cohomology module of configuration spaces of manifolds
Dec
29
comment Maximal trivialising subspace for a vector bundle
@Strongart: I added some clarifying details to my answer. In particular, I think the separation axiom I need is regularity, which follows from locally compact Hausdorff.
Dec
29
revised Maximal trivialising subspace for a vector bundle
Added some clarifying details
Dec
26
comment Maximal trivialising subspace for a vector bundle
@Strongart: I don't think we can say that there is a open neighbourhood of $x$ which does not intersect $Y$ and is a trivial subspace, without assuming $X$ is locally contractible or something similar. However, any vector bundle over a point is trivial, hence my argument involving the disjoint union topology.
Dec
24
answered Maximal trivialising subspace for a vector bundle
Dec
23
comment algebraic structure of Integral Steenrod squares
I'm not sure you need the Leibniz rule, since these are compositions rather than products. I started writing an answer but got confused by mod 2 binomial coefficients. My feeling is that you will get some expression like you stated, but the coefficients will all be either $0$ or $1$.
Dec
23
comment algebraic structure of Integral Steenrod squares
Perhaps you have tried this already, but writing $Sq^a_\mathbb{Z} Sq^b_\mathbb{Z} = \beta Sq^{a-1}\rho_2 \beta Sq^{b-1} \rho_2 = \beta Sq^{a-1} Sq^b \rho_2$ and then trying to use the Adem relation for $Sq^{a-1} Sq^b$ might get you somewhere.
Dec
22
comment Is it known whether this space is a suspension space?
This is true, since (i) localization commutes with homotopy pushouts, and (ii) a 2-connected suspension is a suspension of a 1-connected space, by the argument in Lemma 3.6 of Berstein and Hilton