12,176 reputation
22569
bio website homepages.abdn.ac.uk/…
location Aberdeen, United Kingdom
age
visits member for 4 years, 11 months
seen 2 hours ago

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


2d
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 $X$.
2d
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
Jun
9
awarded  Revival
Jun
9
answered Reference request: Flipping the factors in the Künneth formula
Jun
5
comment Persistence barcodes and spectral sequences
@SeanTilson: Thanks. No, I don't think I am. Could you provide a reference?
Jun
5
awarded  Nice Question
Jun
4
awarded  Popular Question
Jun
4
asked Persistence barcodes and spectral sequences
May
28
comment Acyclic complexes for extraordinary cohomology theories
It's not quite correct to say the $E_2$ page is zero: you have the coefficients of your homology theory (i.e., the value of $E_\ast$ on a point) in the $p=0$ column. Hence the spectral sequence collapses and $X$ has the $E$-homology of a point. So I think a simple change of wording will make Qiaochu happier.
May
26
comment Kunneth formula for cohomology
@Sigur: If you wanted to compute the cohomology of $A\otimes B\otimes C$, one way would be to apply the above Kunneth sequence twice: once to compute the cohomology of either $A\otimes B$ or $B\otimes C$, then again to compute the cohomology of $A\otimes B\otimes C$.
May
26
comment What's the name of this branched covering?
Viewed as a $2$ dimensional orbifold, I think what you have is the spindle $S^2(2,2)$. See p.13 of these slides, for example: www-sop.inria.fr/geometrica/collaborations/OrbiCG/…
May
25
answered stable splitting into a wedge sum
May
25
comment stable splitting into a wedge sum
What's the map from $X$ to its suspension?
May
24
accepted Non-orientable $6$-manifold with $H_4(M)=\mathbb{Z}/2$?