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visits | member for | 3 years, 8 months |
seen | 29 mins ago | |
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Jul 14 |
reviewed | Approve teaching tag wiki excerpt |
Jul 8 |
reviewed | Approve geometric-measure-theory tag wiki excerpt |
Jun 23 |
reviewed | Approve Why is differential Galois theory not widely used? |
Jun 9 |
reviewed | Approve rough-paths tag wiki excerpt |
Jun 9 |
reviewed | Approve rough-paths tag wiki |
Jun 4 |
reviewed | Approve Generalization of Krull dimension for commutative rings |
May 29 |
reviewed | Approve A question on an set of 8 matrices related to the SU(3) generators |
May 29 |
answered | Topologies on spaces of distributions and test functions |
May 29 |
reviewed | Approve Schubert Polynomials for Complex Projective Space |
May 27 |
answered | Searching for $C^*$ |
May 27 |
reviewed | Approve How hard is it to make a differential operator Hermitian? |
May 25 |
reviewed | Approve How to understand a solenoid? |
May 24 |
reviewed | Approve Determinant of some covariance matrix (Gaussian kernel process) |
May 22 |
reviewed | Approve Is g( ) rational if it looks that way on a large rational subset? |
May 21 |
awarded | Enlightened |
May 21 |
awarded | Nice Answer |
May 20 |
comment |
How bad can $\pi_1$ of a linear group orbit be?
I believe I understand how §5 and §6 show that $j^{−1}(L_vL′)$ and $j^{−1}(L_v\cap L′)$ are extensions: $$ 1→j^{−1}(L′)→j^{−1}(L_vL′)\xrightarrow{p∘j}A→1 $$ $$ 1→j^{−1}(j(M))→j^{−1}(L_v\cap L′)\xrightarrow{[\operatorname{mod}j(M)]∘j}F→1 $$ where $A=p(L_v)$ is (connected abelian Lie) × (free abelian of finite rank), and $F$ is finite. Embarrassingly I don't understand how §7 uses this to analyze $j^{−1}(L_v)$ and its $π_0$. Hopefully what I'm missing (perhaps some use of $1→L_v\cap L'→L_v→(L_vL')/L'→1?)$ was just "too obvious to bother mentioning". |
May 19 |
revised |
Examples of TVS with no non-trivial open convex subsets
(statement was trivially false for finite-dimensional spaces) |
May 19 |
answered | Examples of TVS with no non-trivial open convex subsets |
May 19 |
comment |
How bad can $\pi_1$ of a linear group orbit be?
Encore merci. Some (hopefully) nitpicking before I can begin to claim I understand your argument. Would you agree that: 1. In §1 of the proof, you need not really relax the hypothesis that $G$ is simply connected (for, modding out a connected subgroup does not change that)? 2. In §3, "$j(G)\subset H$" should be "$j(G)\subset L$"? 3. In §4, the very last $L$ should be $L_a$? 4. In §5, "virtually connected" should be "connected"? 5. In §6, the last sentence should be "so $\operatorname{Ker}(j)M$ has finite index in $j^{-1}(L'\cap H)$"? |