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bio website homepages.abdn.ac.uk/…
location Aberdeen, United Kingdom
age
visits member for 4 years, 7 months
seen 13 hours ago

Lecturer at University of Aberdeen, with interests in Algebraic and Differential Topology and their applications.


2d
comment 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
comment 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
comment Two H-space 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
comment Two H-space 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
comment 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
comment 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 counter-examples 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
comment 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
comment Lusternik-Schnirelmann Theorem
@Vrouvrou: I'm not sure what you are asking, can you give a page reference?
Jan
21
comment Lusternik-Schnirelmann Theorem
Yes, Theorem 1.15.
Jan
21
comment Lusternik-Schnirelmann Theorem
See my edit for a more precise reference.
Jan
21
revised Lusternik-Schnirelmann Theorem
Gave more precise reference
Jan
21
answered Lusternik-Schnirelmann Theorem
Jan
16
answered References for Eilenberg-Zilber shuffle product
Jan
16
comment cohomology algebra of braid spaces, configuration spaces
Their methods do not give the product structure on cohomology, however.