bio  website  homepages.abdn.ac.uk/… 

location  Aberdeen, United Kingdom  
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visits  member for  4 years, 7 months 
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Lecturer at University of Aberdeen, with interests in Algebraic and Differential Topology and their applications.
2d

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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! 
Feb 18 
revised 
Pairing of cohomology and homology Künneth formulas
added generalisation 
Feb 17 
asked  Pairing of cohomology and homology Künneth formulas 
Feb 14 
revised 
Actions of cofibrations and induced maps of cofibres
typos, and added some more explanation 
Feb 13 
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cohomology of orthogonal group of integers
Is an element of your first group a $k\times k$ matrix with integer entries? If so then I think this is $Gl_k(\mathbb{Z})$, which might help you get started looking for references. 
Feb 13 
asked  Actions of cofibrations and induced maps of cofibres 
Feb 2 
answered  Ambient isotopy of the diagonal submanifold in product space 
Feb 1 
answered  integral or rational cohomology of real grassmannians 
Jan 24 
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LusternikSchnirelmann Theorem
@Vrouvrou: I'm not sure what you are asking, can you give a page reference? 
Jan 21 
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LusternikSchnirelmann Theorem
Yes, Theorem 1.15. 
Jan 21 
comment 
LusternikSchnirelmann Theorem
See my edit for a more precise reference. 
Jan 21 
revised 
LusternikSchnirelmann Theorem
Gave more precise reference 
Jan 21 
answered  LusternikSchnirelmann Theorem 
Jan 16 
answered  References for EilenbergZilber shuffle product 
Jan 16 
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cohomology algebra of braid spaces, configuration spaces
Their methods do not give the product structure on cohomology, however. 