bio  website  homepages.abdn.ac.uk/… 

location  Aberdeen, United Kingdom  
age  
visits  member for  4 years, 9 months 
seen  4 mins ago  
stats  profile views  4,548 
Lecturer at University of Aberdeen, with interests in Algebraic and Differential Topology and their applications.
2h

comment 
stable splitting into a wedge sum
What's the map from $X$ to its suspension? 
18h

accepted  Nonorientable $6$manifold with $H_4(M)=\mathbb{Z}/2$? 
1d

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Nonorientable $6$manifold with $H_4(M)=\mathbb{Z}/2$?
@user51223: This question came up when studying mod 2 cohomology classes realizable by immersions/embeddings. 
1d

comment 
Nonorientable $6$manifold with $H_4(M)=\mathbb{Z}/2$?
@GabrielC.DrummondCole: Thanks, I think it works! 
2d

asked  Nonorientable $6$manifold with $H_4(M)=\mathbb{Z}/2$? 
May 12 
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Triangulations of submanifolds of smooth manifolds
@IgorRivin: That's a good question, I confess to not being an expert. Here's what I know: $\operatorname{Emb}(M,N)$ is open in $C^\infty(M,N)$, and dense if $2m\le n$. Also, the space of topologically stable maps $M\to N$ is open and dense in $C^\infty(M,N)$ (the ThomMather theorem). I believe it follows that every embedding is isotopic to a topologically stable, hence triangulable, embedding. 
May 11 
awarded  Necromancer 
May 10 
answered  What are the uses of the homotopy groups of spheres? 
May 10 
answered  Triangulations of submanifolds of smooth manifolds 
May 5 
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Reference request: Flipping the factors in the Künneth formula
@SeanTilson: I disagree. This is exactly the kind of thing you would not want to reprove in a paper, hence seems like a totally reasonable reference request. 
Apr 21 
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Studying topology: which first, algebraic or differential?
I downvoted this otherwise excellent list, but I must admit it was an emotional reaction to the negative comments about Hatcher's book. Now the software won't allow me to reverse my downvote, unless the answer is edited. Perhaps this will motivate you to remove these subjective comments? ;) 
Apr 21 
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Example s.t. the unbased loopspace is not $\Omega X \times X$
A convenient lowtech reference for the "standard fact" is in V. L. Hansen, On the fundamental group of a mapping space. An example, Compositio Mathematica 28, 1974. 
Apr 7 
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Cohomology operators inducing local basis of $1$forms
What do you mean by local basis here? If you just want a basis of $\Omega^1(M)$ of the given type, then it seems like $H^1(\Omega(M),\partial)=0$ is a necessary and sufficient condition. 
Apr 3 
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Toral rank conjecture
@MyIsmail: I think the $2$ in the second bound should be $1/2$. 
Mar 25 
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Homotopy of orthogonal groups in the unstable range
Section 1 of the paper maths.ed.ac.uk/~aar/papers/levsph.pdf contains a similar result for $SO$. Perhaps the argument there works for $O$ also? 
Mar 19 
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cohomology of the orbit space of a group action
Presumably this can be promoted to a statement about graded algebras? And is it also true if $G$ is invertible in $F$? 
Mar 17 
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Two Hspace structures on S^3 and [X,S^3] different as groups for each: Explicit Example?
Nice! And you might hope to compute the groups $[S^3\times S^3,S^3]$, using the cofibration sequence $S^3\vee S^3\to S^3\times S^3 \to S^3\wedge S^3 = S^6$. 
Mar 17 
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Two Hspace structures on S^3 and [X,S^3] different as groups for each: Explicit Example?
If $X$ is a closed oriented $3$manifold, then maps $X\to S^3$ are classified by their degree. Since the degree can be detected homologically, and since any multiplication $m:S^3\times S^3\to S^3$ must do the obvious thing on third homology, I think all the groups are isomorphic when $X$ is an oriented $3$manifold. (I leave this comment in case anyone else was thinking of using Hopf's theorem.) 
Feb 22 
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Pairing of cohomology and homology Künneth formulas
@user43326: Good point. Well, it's not trivial to me! But I would expect (if true) it should be proved somewhere already. 
Feb 21 
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Pairing of cohomology and homology Künneth formulas
The pairing itself is canonical, but you are right that the way Tor sits in the homology depends on a choice of splitting. I think the statement could still be true, but would also accept counterexamples as answers! 