11,800 reputation
3866
bio website wwwmath.uni-muenster.de/…
location Münster
age 37
visits member for 3 years, 6 months
seen yesterday

I am a mathematician based in Münster, Germany. A fellow MO user once described me as a ''very homotopy-theoretic geometric topologist'' and I largely approve this description.


Apr
9
awarded  Enlightened
Apr
9
awarded  Nice Answer
Mar
14
comment What is the group of pointed homotopy classes of maps from $S^3 \times S^3$ to $S^3$?
Nice answer. I gues you mean $HP^{\infty}$, not $HP^4$.
Feb
26
answered Integral formula for Euler class
Feb
13
comment On a homological finiteness condition
@Fernando, Michal: yes, the problem is the direction of the arrow. But the paper you linked to seems very interesting.
Feb
13
revised On a homological finiteness condition
edited tags
Feb
12
revised On a homological finiteness condition
added 97 characters in body
Feb
12
awarded  Nice Question
Feb
12
comment On a homological finiteness condition
@Igor: I guess you mean that for each finite CW, there is a duality group and a map $BG \to X$ (not $X \to BG$). It is fairly easy to produce, for each finite sequence of finite abelian groups, a finite complex that has the sequence of groups as homology: take a wedge of suitable Moore spaces. So: if what you say is true, then any finite sequence of finitely generated abelian groups is the homology of a duality group.
Feb
12
comment On a homological finiteness condition
@Misha: my gut feeling is that I should not try to kill $\pi_1$. If $X$ is aspherical, I cannot have a simply connected $Y$ with the desired properties. ''I can explain why'': it would be welcome if you share your insight -:))
Feb
12
revised On a homological finiteness condition
added 456 characters in body
Feb
12
comment On a homological finiteness condition
@Vidit: you can assume that $X$ is a simplicial complex, but I do not think this makes it much easier.
Feb
12
comment On a homological finiteness condition
yes: in order to apply Walls theory, one needs a finite domination and in particular finitely presented fundamental group. Moreover, I do seek for a homology isomorphism, not a homotopy equivalence; and I have no control on the groups, so no chance to rule out the finiteness obstruction. I think it is really a different problem.
Feb
12
revised On a homological finiteness condition
added 2 characters in body; edited title
Feb
12
comment On a homological finiteness condition
This was my first idea, but I did not find anything that is really close to what i am looking for.
Feb
12
asked On a homological finiteness condition
Feb
2
comment Space of embeddings of circle in a surface
There is a result by Gramain (1973, Le type d'homotopie...) which says that the space $Emb((S^1,v),(M,w))$ of embeddings with prescribed behaviour on a fixed unit tangent vector has contractible components, for each compact surface. His proof is purely topological. This should imply what you are looking for, though I do not see it immediately.
Feb
2
comment Adams' theorems on the Hopf-Whitehead J-homomorphism
If I want to show that the $J$-homomorphism is injective on $\pi_{8n}$, I have to show that a homotopy $8n+1$-sphere is stably parallelizable, but unfortunately the only argument known to me uses the fact on the $J$-homomorphism. So it seems to be circular.
Feb
2
comment Adams' theorems on the Hopf-Whitehead J-homomorphism
Ok, now I understand what you are saying. But I do not see how you turn the disc into a standard disc, i.e. why the ''framing does extend''.
Feb
2
awarded  Nice Question