bio  website  homepages.abdn.ac.uk/… 

location  Aberdeen, United Kingdom  
age  
visits  member for  4 years, 11 months 
seen  2 hours ago  
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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/HalperinCarlsson Conjecture
added comments from Greg Lupton and link to notes of Vicente Munoz 
Jun 29 
comment 
Special Case of the Toral Rank/HalperinCarlsson 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 
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Special Case of the Toral Rank/HalperinCarlsson 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 welldeveloped 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 'nonintuitive' 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 
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What is the $\mathbb Z/2$cohomology of $\mathrm B^n(\mathbb Z/2)$?
The original reference is: Serre, JeanPierre, Cohomologie modulo 2 des complexes d'EilenbergMacLane. (French) Comment. Math. Helv. 27, (1953). 198–232. 
Jun 19 
answered  Special Case of the Toral Rank/HalperinCarlsson 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 
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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 
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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 
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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: wwwsop.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  Nonorientable $6$manifold with $H_4(M)=\mathbb{Z}/2$? 