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Jan
2
comment Why are abelian groups amenable?
@Misha: There was a small mistake in my proof (it didn't handle well the case when $g_i$ has finite order), which I've fixed now. It seems that this may have been your objection. If not, could you clarify what the issue is?
Jan
2
revised Why are abelian groups amenable?
corrected proof in case when g_i has finite order
Jan
2
comment Principal bundles that can't be detected by spheres
Any other circle bundle over the 2-torus will work as well, won't it?
Jan
2
revised Why are abelian groups amenable?
add proof of main claim
Jan
1
answered Rings that inject in all p-adic integers
Nov
12
answered equivariant embeddings from the k-th configuration space to the k+1-th configuration space
Nov
7
comment Reference Request: Irreducibles of the regular representation of the permutation group is absolutely irreducible
@phys In even more simple terms: yes, the irreducible representations of the symmetric group over $\mathbb{R}$ remain irreducible when you extend them to $\mathbb{C}$.
Oct
29
awarded  Good Answer
Oct
29
reviewed Approve Proofs without words
Oct
13
reviewed Approve An inequality for certain characters
Oct
12
awarded  Yearling
Sep
29
comment Is there a notion of “flat vector bundle over a topological space”?
I don't understand this argument. Doesn't this just amount to the (true) remark that "Another name for a flat vector bundle is a local system"?
Aug
25
reviewed Approve Precise interpretability strength of $\mathcal P_{DF}(\omega)$ and $L_{\omega_1^{CK}}$
Aug
18
comment Strategies for proving a category is Noetherian?
Regarding the last sentence and Steven's comment: to prove that FI is Noetherian, the Grobner methods (using that OI -> FI is finite) feel more modern than our original proof in Church-Ellenberg-Farb-Nagpal. (For this question, though, CEFN could still be valuable just for providing another approach to Noetherianness.) In any case, these methods certainly work over Z. In contrast, I believe the result of Nagpal-Sam-Snowden in your third paragraph does not apply except over C; see Question 1.5(3) and the remark following 5.3. Perhaps one of the authors can clarify this?
Aug
12
reviewed Approve A generalization of the Powers-Stormer inequality
Aug
6
comment Suitable reference on smooth manifolds for qualifying exam study?
You should consider reading Bott & Tu's "Differential Forms in Algebraic Topology": not as a resource for smooth manifolds, nor as a resource for algebraic topology, but for the beautiful interplay between them. I benefited greatly from reading it in graduate school, not least because it broadened my perspective on what techniques might be applied to what problems.
Jul
17
comment The evaluation fibration of a transitive, effective topological group action
Do you mean "fibration" or "fiber bundle"? en.wikipedia.org/wiki/Fibration en.wikipedia.org/wiki/Fiber_bundle
Jul
17
comment Properties of loop space functor from homotopy types to group objects in homotopy types
I'm not an expert in any of this material, but it seems to me that it might be helpful to learn about classifying spaces before jumping to $(\infty,1)$-categories.
Jul
17
comment When to postpone a proof?
Your Example 1 is dragging this discussion in the wrong direction, since everyone is going to agree with it: who would object to stating the main theorems in the introduction? The real question is about the structure of arguments within the body of the paper, and when it is appropriate to postpone a proof there. This is an important question, which too many authors neglect to think about when outlining their papers; I hope we'll get to hear a discussion on this point.
Jul
13
reviewed Approve Why is the fundamental group of a compact Riemann surface not free ?