10,664 reputation
12262
bio website staff.ncl.ac.uk/mark.grant
location Newcastle upon Tyne, United Kingdom
age
visits member for 4 years
seen 18 hours ago

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


2d
comment Terminology for beads/necklace/bracelet problem
MO is for "research level" mathematics, and MSE is for mathematics of all levels. Of course, it's open to interpretation what "research level" means (and it certainly means different things to different people). Anyway, lots of very competent mathematicians answer questions at MSE, and questions such as yours might get a better reception there. (Although it looks like you might already have an answer here).
2d
comment Terminology for beads/necklace/bracelet problem
What you are doing is enumerating the cosets $\Sigma_N/H$, where $\Sigma_N$ is the group of permutations on $N$ letters and $H$ is the subgroup generated by cyclic permutations and reflection. I don't know of a name for this. (I also think this question would be a better fit for math.stackexchange.com.)
2d
answered In a fibration, can a deformation retraction of the base be lifted to the total space?
Aug
16
answered Constructing a space with prescribed cohomology ring
Aug
7
comment K-theory of $\mathbb{RP}^\infty$
J.F. Adams, Vector fields on spheres. Ann. of Math. (2) 75 1962 603–632. See Theorem 7.3 there.
Aug
6
answered Pseudo-manifolds and homology
Aug
4
accepted Homology exponents for $QX$
Aug
2
awarded  Yearling
Jul
31
comment Connected representant of a framed cobordism class (reference needed)
Ah, OK. Where does your proposed proof for $n>0$ break down when $n=0$?
Jul
31
answered Connected representant of a framed cobordism class (reference needed)
Jul
31
answered Splitting the Hopf map in two
Jul
31
comment Splitting the Hopf map in two
Note that there is nothing special about the Hopf map here. Any map $h: S^3\to S^2$ is null-homotopic when restricted to the equator, since the inclusion $S^2\hookrightarrow S^3$ is null-homotopic. So there will be a map $h':S^3\vee S^3\to S^2$ which expresses $h$ as a sum. In general, though, $h'$ will depend on the null-homotopy. Choosing either of the standard null-homotopies will no doubt result in one of $f$ or $g$ being null and the other being $h$.
Jul
25
comment Milnor's exact sequence and a certain proof
Regarding the description of the connecting map $d$: my coauthors and I needed this and couldn't find a reference, so wrote out "actual argument" in our preprint arxiv.org/abs/1312.7166 (it's the $n=2$ case of Proposition 2.1 there).
Jul
20
answered Criterion for deloopable based map
Jul
18
comment Topological relationships between family of transversal intersections of manifolds
Oscar beat me to it by a few minutes, but I thought I'd post the answer anyway in case you find the references useful.
Jul
18
answered Topological relationships between family of transversal intersections of manifolds
Jul
14
comment Proof or citation?
Maybe you could include a sentence or two explaining why it is trivial? That way you can help your readers reconstruct the proof, without appearing patronizing.
Jul
14
revised natural co-product on minimal Sullivan model
lengthened short answer, formatting; typo
Jul
14
answered natural co-product on minimal Sullivan model
Jul
10
answered An analogue of cabling for configuration spaces