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12364
bio website staff.ncl.ac.uk/mark.grant
location Aberdeen, United Kingdom
age
visits member for 4 years, 4 months
seen 7 hours ago

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


23h
awarded  Nice Question
2d
comment Homotopical nilpotency
I don't know that I would expect such a characterization to exist, given that for groups the condition of being nilpotent of class 2 already seems quite elementary.
Nov
20
revised Configuration space like subspace of sphere product
added 2 characters in body
Nov
20
comment Configuration space like subspace of sphere product
I think the algebraic map actually goes to $\mathbb{R}^{n+1}$, hence the discrepancy in our dimensions.
Nov
20
answered Configuration space like subspace of sphere product
Nov
19
comment Robotics, Cryptography, and Genetics applications of Grothendieck's work?
It may be worth noting that in that chapter Farber is surveying work of Gal: journals.impan.pl/cgi-bin/doi?cm89-1-4
Nov
14
answered Definition of Milnor exact sequence and complex-oriented generalized cohomology of $\mathbb{C}P^{\infty}$
Nov
12
revised Realization of second Stiefel-Whitney class
changed i to 1
Nov
12
answered Realization of second Stiefel-Whitney class
Nov
12
comment Degree of Map between Pseudomanifold
I presume that you can prove well-definedness in the same way as in the smooth case (by showing that it's homotopy invariant and that any $n$-simplex is mapped onto any other $n$-simplex by a homeomorphism isotopic to the identity) but I haven't time to check the details. By the way, if $N$ is not compact then the degree will be zero (since $f(M)$ is compact so $f$ is not surjective). Milnor notes this on p.20).
Nov
12
comment Degree of Map between Pseudomanifold
@gaoxinge: I don't see why not. If $M$ is compact, then the inverse image of any simplex in $N$ under a simplicial map will be a finite union of simplices. So as long as $M$ and $N$ are oriented, we get a finite sum of $+1$s and $-1$s.
Nov
12
comment Degree of Map between Pseudomanifold
I think you can define the degree to be as in Exercise F.1 on Spanier page 207 (which is entirely analogous to how Milnor does it in the smooth case). The point is your pseudo manifold doesn't have to be finite to have an orientation.
Nov
7
comment Homotopy groups of $MO(2)$
Thank you, both. Which version of the unstable Adams spectral sequence are you using, Tyler? I would very much like to check what $\pi_7$ is, if possible.
Nov
6
asked Homotopy groups of $MO(2)$
Nov
6
comment The relation between group cohomology and the cohomology of the classifying space
Are you familiar with Stasheff's article maths.ed.ac.uk/~aar/papers/stasheff5.pdf ? The references there might answer your question.
Oct
14
accepted Minimal models with local coefficients
Sep
30
awarded  Explainer
Sep
7
awarded  Necromancer
Sep
7
comment Idea and intuition behind Penrose transform
It might help to say why the Wikipedia page doesn't do what you want.
Sep
6
comment the algebraic theory of obstruction of a homology theory
The obstruction is the submodule $\operatorname{Im} (d\circ d)$. Without more context it seems difficult to say more.