9,961 reputation
11958
bio website staff.ncl.ac.uk/mark.grant
location Newcastle upon Tyne, United Kingdom
age
visits member for 3 years, 8 months
seen 12 hours ago

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


Apr
11
awarded  Popular Question
Apr
5
answered How can I prove that Hopf fibrations are the only ones with fiber, total space and base space homeomorphic to spheres?
Apr
5
revised rationalization of classifying spaces
fixed spelling of McCleary
Apr
5
comment rationalization of classifying spaces
Two nilpotent spaces with finite Betti numbers are rationally homotopy equivalent if and only if they have isomorphic minimal models. So the above argument should work, as long as there are only finitely many $y_i$ in each even degree.
Apr
4
answered rationalization of classifying spaces
Apr
3
comment Fake projective spaces
Hi Diarmuid, thanks for fixing the link.
Apr
3
reviewed Approve suggested edit on Fake projective spaces
Apr
2
comment What does it mean to speak of a homotopy fibration sequence?
At the level of spaces, not every map $f:X\to Y$ is a fibre inclusion (in particular, the homotopy fibre would have to be homotopy equivalent to a loop space $\Omega Z_f$). So probably the fact that they are working with spectra matters here.
Apr
1
comment Extending binary operation used by homotopy classes
Your operation is only associative up to homotopy (perhaps you want to talk about end-point preserving homotopy classes of paths, in which case the fundamental groupoid may be a more natural object to study). The lack of symmetry here is a bit unsettling, too. You could alternatively get a partial monoid by declaring $p\ast q$ to be defined only when $p(1)=q(0)$.
Mar
31
comment Group extensions isomorphic as groups
Do you know an example of two different cohomology classes which are equivalent in this way?
Mar
31
comment The cohomology plus what characterizes the rational homotopy type?
You're welcome. I don't understand these structures well enough to give a definitive answer to your question, but my suspicion is the answer is no. It is remarked on p12 of the linked preprint the relation of the operation $m_3$ with Massey triple products. Presumably the operation $m_n$ is related to Massey products of length $n$ in the same way. Now, I can imagine that there are spaces whose Massey products up to length $n$ all vanish, but which has a non-vanishing Massey product of length $(n+1)$.
Mar
30
reviewed Approve suggested edit on Translation of “Über kompakte homogene Kählersche Mannigfaltigkeiten”
Mar
30
answered The cohomology plus what characterizes the rational homotopy type?
Mar
27
comment A cohomology associated to a 1- form
What happens in the intermediary case between "nowhere zero" and "zero"?
Mar
26
comment Equivariant Formality
@Oliver: I don't know, sorry. Such an $\mathcal{A}$ would correspond to a space with $n$ path components. You could take a model of each component separately, but then it may be that the group action mixes them up somehow.
Mar
25
answered Equivariant Formality
Mar
25
comment I don't understand behavior of this integral, help!
@მამუკაჯიბლაძე: This is quite far from my area, so I'd rather leave that to someone else. I'd advise against the words "I don't understand..." and "help!" in the title though, as many people skimming the question list might mistake your question for an undergraduate plea for help with homework (which it clearly isn't).
Mar
25
comment I don't understand behavior of this integral, help!
Can I suggest changing the title to something more descriptive?
Mar
23
answered Relative Serre spectral sequences?
Mar
20
comment Spectral sequences and Koszul complexes in Deformation Theory
Dear Pedro, not a problem. I'm afraid this is not really my area, but your question appears to be well-written, and I hope an expert can give you an answer.