12,226 reputation
22669
bio website homepages.abdn.ac.uk/…
location Aberdeen, United Kingdom
age
visits member for 5 years
seen 4 hours ago

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
comment 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
comment 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
comment Extending an homotopy, knowing the two base functions extend
Probably you want the inclusion $A\subseteq B$ to be a cofibration.
Jul
14
comment Regularity of maps in algebraic topology for manifolds
You're welcome @Paul-Benjamin. 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 would-be 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 counter-example.
Jul
4
comment 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
comment 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/Halperin-Carlsson Conjecture
added comments from Greg Lupton and link to notes of Vicente Munoz
Jun
29
comment Special Case of the Toral Rank/Halperin-Carlsson 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
comment Special Case of the Toral Rank/Halperin-Carlsson 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 well-developed rational surgery theory for answering this type of question (see Theorem 3.2 in the book, or here: mathoverflow.net/questions/115911/…)
Jun
24
comment What is the 'non-intuitive' 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
comment What is the $\mathbb Z/2$-cohomology of $\mathrm B^n(\mathbb Z/2)$?
The original reference is: Serre, Jean-Pierre, Cohomologie modulo 2 des complexes d'Eilenberg-MacLane. (French) Comment. Math. Helv. 27, (1953). 198–232.
Jun
19
answered Special Case of the Toral Rank/Halperin-Carlsson Conjecture