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visits | member for | 5 years, 7 months |
seen | May 9 at 13:37 | |
stats | profile views | 3,157 |
Mar 29 |
comment |
Has any attempt been made to classify finite groupoids?
Extensions of $G$ by a nonabelian $M$ are classified by cohomology of $G$ with coefficients in what the ancients called a crossed module; i.e. by homotopy classes of maps from $BG$ to the delooping of $\mathrm{Aut}(BM)$. Since $M_{12}$ has no center, $\mathrm{Aut}(BM_{12}) \cong \mathrm{Out}(BM_{12}) \cong \mathbf{Z}/2$. That means there can be no nontrivial extensions of a group like $\mathrm{SL}_3(\mathbf{F}_3)$ or $\mathrm{PGL}_3(\mathbf{F}_3)$ by $M_{12}$, right? |
Mar 17 |
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Does a polytope have a self-indexing shelling?
Thanks Richard, I hadn't seen this question. Besides not allowing deformations, another difference is that I am curious about shellings that do not come from linear functions. |
Mar 17 |
asked | Does a polytope have a self-indexing shelling? |
Mar 16 |
comment |
What if the low-degree cohomology of a $G$-module and all its restrictions vanish?
It looks like this is a 1959 result of Rim. Thanks Chris. |
Mar 16 |
accepted | What if the low-degree cohomology of a $G$-module and all its restrictions vanish? |
Mar 15 |
asked | What if the low-degree cohomology of a $G$-module and all its restrictions vanish? |
Feb 10 |
awarded | Popular Question |
Feb 9 |
answered | Calculating Mayer-Vietoris efficiently |
Feb 9 |
comment |
Calculating Mayer-Vietoris efficiently
"Suppose that I know all of the $H^*(U_i)$'s, and all of the restriction maps between them, and I would like to compute $H^*(X)$." Note that even when there are just two open sets $U_1$ and $U_2$ and their intersection $U_1 \cap U_2$, this data only determines one-third of the maps in the Mayer-Vietoris long exact sequence. You get an upper bound on $H^*(U_1 \cup U_2)$ but does not determine it in general. A similar problem with the Mayer-Vietoris spectral sequence, is that the data you have supplied is enough to determine the groups on the $E_2$ page but none of the differentials. |
Jan 23 |
accepted | Is mean width a Dehn invariant? |
Jan 23 |
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Is mean width a Dehn invariant?
Ilya, what is the mean width of the 1x1xN^3 box? |
Jan 23 |
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Is mean width a Dehn invariant?
Hi Ilya and Yoav. Have I misunderstood the definition of scissors congruence, or the discussion of mean width on this wikipedia page? en.wikipedia.org/wiki/Hadwiger_theorem |
Jan 23 |
asked | Is mean width a Dehn invariant? |
Jan 13 |
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Exact Functors from Perverse Sheaves
If $0 \to P' \to P \to P'' \to 0$ is a short exact sequence of perverse sheaves, then there is a map $P'' \to P'[1]$ in the derived category making $P' \to P \to P'' \to P'[1]$ into an exact triangle. (I think this is the definition of "admissible" abelian subcategories of triangulated categories given by Beilinson-Bernstein-Deligne section 1.2; in section 1.3 they show the heart of a t-structure is admissible). |
Jan 12 |
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Twisting of the power functor
Hi Dmitry. What does the symbol "D^b(T(k))" mean? |
Dec 17 |
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automorphism of prime order for group of Lie type in
There's an automorphism of Spin(8), of order 3, that does not preserve any pinning. Its fixed-point subgroup is SL(3). I don't know whether it exists in characteristic 3. There is a nice treatment of all characteristic zero examples at www2.bc.edu/mark-reeder/Torsion.pdf |
Dec 14 |
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Does the $(\mathbb Z/2)$-graded isomorphism $E_n \cong E_{n+2}$ have any nice properties?
I didn't mean anything too metaphysical. Since the two-periodic E_n and E_{n+2} operads have actions of O(n) and O(n+2), something you could add to your list of hypothetical "nice properties" is that the isomorphism between them is equivariant for the inclusion O(n) --> O(n+2). Is that true? |
Dec 14 |
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Does the $(\mathbb Z/2)$-graded isomorphism $E_n \cong E_{n+2}$ have any nice properties?
Is there a single operad called E_n? Or is there an interesting connected space of operads called E_n with no distinguished base point? For the nonlinear version (operads in spaces), I hope that the "classifying space of E_n operads" is BO(n). The classifying space of E_n operads in your funny 2-periodic category must be a lot different. Maybe it is BO? |
Nov 24 |
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Is there a cotangent bundle of a stable $\infty$-category?
Thanks Sam. What if I insist that the construction of $T^* C$ should not depend on any monoidal structure $\otimes$? For example it doesn't seem like such a structure is available in part 2. |
Nov 21 |
awarded | Nice Question |