7,521 reputation
1643
bio website people.mpim-bonn.mpg.de/…
location Bonn
age 33
visits member for 5 years
seen 10 hours ago

I am a postdoc at the Max Planck Institute for Mathematics. I did my PhD at Utrecht University under the advisement of Ieke Moerdijk. My thesis was entitled "Categorical Properties of Topological and Differentiable Stacks". My current research interests are applications of higher category, derived geometry, and recently field theory.


2d
comment Are all quotients of a weakly contractible space via a free group action classifying spaces of the group?
If $G$ is a compact Lie group, then any free action on a Tychonoff space is a principal bundle.
Mar
27
comment When does the Borel construction have the homotopy type of a CW-complex?
Thanks, I was just about to send you an email asking about that, I assume you meant double mapping cylinder? I think I'll just send the email :).
Mar
26
comment When does the Borel construction have the homotopy type of a CW-complex?
Actually, using your mapping cone idea, it's probably easiest to work directly with the fat geometric realization of the nerve of the action groupoid $G \ltimes X$. Each of its skeleta, by your above observation, will have the homotopy type of a CW-complex.
Mar
26
comment When does the Borel construction have the homotopy type of a CW-complex?
P.S. I think all topological manifolds also have the homotopy type of a CW-complex as well (when it's 2nd countable).
Mar
26
accepted When does the Borel construction have the homotopy type of a CW-complex?
Mar
26
comment When does the Borel construction have the homotopy type of a CW-complex?
@QiaochuYuan: See my comment on Tyler's answer below.
Mar
26
comment When does the Borel construction have the homotopy type of a CW-complex?
@JohnPardon: Yes, I really mean a CW-complex. I just want it to satisfy Whitehead's theorem.
Mar
26
comment When does the Borel construction have the homotopy type of a CW-complex?
Thanks! The model for $EG$ I am using is the fat geometric realization of the (topologically enriched) nerve of the topological action groupoid $G \ltimes G$. Please correct me if I'm wrong, but I imagine that the same argument goes through by using the skeleta filtration of its fat geometric realization.
Mar
26
asked When does the Borel construction have the homotopy type of a CW-complex?
Mar
26
answered Your favorite surprising connections in Mathematics
Mar
26
comment Smooth maps considered as locally ringed space morphisms?
So what you've actually proven is that the topological spaces embed fully faithfully into locally ringed spaces, by, taking as their structure sheaves the sheaf of $\mathbb{R}$-valued functions, great!
Mar
25
comment A comprehensive functor of points approach for manifolds
@HarryGindi: This is an old question, so maybe you're not interested anymore. However, would you be satisfied if you had a categorical characterization of which sheaves on the site of open subsets of Euclidean spaces and smooth maps are representable by a manifold? If so, I have an answer for you, so let me know.
Mar
24
comment simplicial spaces without degeneracies
Actually, it turns out that there are more problems, e.g. $X_k \times \partial \Delta^k \to X_k \times \Delta^k$ is not a Serre cofibration in general, and the above mentioned T1 property. However, you can get around both of these by using facts in Appendix A of citeseerx.ist.psu.edu/viewdoc/…. I need this fact in a paper I am writing, so the complete write up should appear on the arXiv soon.
Mar
19
comment What is the stalk of a stack?
Yes, but the question was about generalizing from stalks of sheaves of sets to stalks of stacks so, although I agree that what I said may not make sense for sheaves of more interesting objects than sets (like modules), it does answer the question asked.
Mar
19
comment simplicial spaces without degeneracies
Suppose that we are talking about fat geometric realization. For the second question, to deduce to checking that you get a weak homotopy equivalence on $k$-skeleta, you have to argue that any map from a sphere factors through a finite stage of the filtration, but I'm not sure how to argue this without assuming that points are closed, so I think you might need some T1 assumption somewhere?
Mar
19
comment What is the stalk of a stack?
The fiber of the etale-space $L(F) \to X$ of a sheaf $F$ over $X$ at a point $x$ IS precisely the stalk $F_x.$ These are one and the same.
Mar
10
awarded  Yearling
Mar
9
answered Topological Grothendieck Construction
Feb
26
comment Based loop groups as stacks?
@Oliver: May I ask why you keep coming back to whether or not the object you construct is "finite dimensional" in some sense? What do you want to do with it?
Feb
26
comment Based loop groups as stacks?
@QiaochuYuan: I've fixed this now.