bio  website  homepages.abdn.ac.uk/… 

location  Aberdeen, United Kingdom  
age  
visits  member for  5 years 
seen  4 hours ago  
stats  profile views  4,632 
Lecturer at University of Aberdeen, with interests in Algebraic and Differential Topology and their applications.
4h

comment 
Manifold approximations to $BO(3)$
@user51223: I want something I can at least compute the integral cohomology of. Following Allen's suggestion, $G_3(\mathbb{R}^6)$ might be in this category (although I've not found an easy reference for that yet). 
5h

awarded  Yearling 
1d

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Indecomposable commutative rings
By the definition of indecomposable, any such decomposition must have all but one of the factors $0$. Am I missing something? 
2d

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Manifold approximations to $BO(3)$
@AllenHatcher: That's a good point. I guess I was hoping for something similar to the Dold manifolds, using some nice approximations to $BSO(3)$. Perhaps in general one has to look at finite Grassmannians, though. I may delete the question. 
2d

revised 
Manifold approximations to $BO(3)$
added closed condition 
2d

comment 
Manifold approximations to $BO(3)$
@JasonStarr: Yes, I intended the manifolds to be closed, thanks for this. I'll edit. 
2d

asked  Manifold approximations to $BO(3)$ 
Jul 30 
answered  The evaluation fibration of a transitive, effective topological group action 
Jul 27 
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Extending an homotopy, knowing the two base functions extend
Probably you want the inclusion $A\subseteq B$ to be a cofibration. 
Jul 14 
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Regularity of maps in algebraic topology for manifolds
You're welcome @PaulBenjamin. There's no need to close the question (you can accept an answer, but in my opinion people are often too quick to do this as it discourages other wouldbe answerers). 
Jul 14 
answered  Regularity of maps in algebraic topology for manifolds 
Jul 14 
comment 
Homological vs. cohomological dimension of a group/space
For Q3), I don't think $BG$ with $G$ acyclic is necessarily contractible. Acyclic usually means trivial homology with integer coefficients, so Higman's group is a counterexample. 
Jul 4 
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Is the Gysin morphism equivariant?
Smooth maps $g: M\to X$ and $j: N\to X$ are transverse if whenever $g(m)=j(n)=x$ then the images of the differential of $g$ at $m$ and the differential of $j$ at $n$ together span the tangent space at $x$ of $X$. 
Jul 4 
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Is the Gysin morphism equivariant?
The answer is yes if $G$ acts by diffeomorphisms, since then each $g$ is transverse to $j$. I don't have these books to hand to check, but I'm sure you'll find a proof in either E. Dyer's "Cohomology Theories" or W. Fulton's "Intersection Theory" 
Jun 29 
revised 
Special Case of the Toral Rank/HalperinCarlsson Conjecture
added comments from Greg Lupton and link to notes of Vicente Munoz 
Jun 29 
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Special Case of the Toral Rank/HalperinCarlsson Conjecture
BTW, I'm not really an expert in the TRC, but I know a couple...I'll email them to alert them of your question. 
Jun 29 
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Special Case of the Toral Rank/HalperinCarlsson Conjecture
Looking at the proof of 7.17, it seems that if $X'$ can be chosen to be a compact manifold, then the action is smooth and free by construction ($X'$ is the total space of a smooth principal $T^n$bundle). However, I'm not sure we can always find a manifold in the rational homotopy type. There is a welldeveloped rational surgery theory for answering this type of question (see Theorem 3.2 in the book, or here: mathoverflow.net/questions/115911/…) 
Jun 24 
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What is the 'nonintuitive' part in sphere eversion (turning inside out)?
@Pacerier: I never said that I did! But I have no reason to doubt that the MO user Bill Thurston was the illustrious mathematician of the same name. 
Jun 22 
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What is the $\mathbb Z/2$cohomology of $\mathrm B^n(\mathbb Z/2)$?
The original reference is: Serre, JeanPierre, Cohomologie modulo 2 des complexes d'EilenbergMacLane. (French) Comment. Math. Helv. 27, (1953). 198–232. 
Jun 19 
answered  Special Case of the Toral Rank/HalperinCarlsson Conjecture 