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 Yearling
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Mar
28
awarded  Yearling
Jan
12
awarded  Revival
Jan
1
comment If $f$ is an immersion and $g$ is a submersion, then is $g \circ f $ a local diffeomorphism?
I had not put this much thought into it. Thanks a lot, especially for the last bit.
Jan
1
accepted If $f$ is an immersion and $g$ is a submersion, then is $g \circ f $ a local diffeomorphism?
Dec
8
awarded  Inquisitive
Nov
11
comment Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
Should have said this yesterday. Is the map you asked for just obtained by shifting the last $(n-k)$ vectors in $A$ to the first $n-k$ vectors and then listing the remaining $k$ vectors?
Nov
10
accepted Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
Nov
10
comment Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
Thanks a lot for your effort. That is very comprehensive!!!
Nov
10
comment Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
@Thanks for your response. Nope. I am not able to explicitly reason this out. I do vaguely understand what you are trying to teach me. But I am still lost mostly. Is $\alpha$ a sort of projection map? and did you mean $E = <v_1,...,v_k>$??
Nov
10
comment Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
I was working with the Grassmannian as a homogeneous space obtained by the group action of orthogonal group, actually I need to prove that too.
Nov
10
asked Diffeomorphism between the Grassmannian manifolds $\mathbf{Gr}(n,k)$ and $\mathbf{Gr}(n,n-k)$.
Nov
4
comment Help with terminology
Thanks. I had given up hope on this one. But can you point me to a specific chapter where this is discussed.
Nov
4
comment Geometric intuition for the Weingarten map
It is the tangent space to the surface $M$ at the point $x$, in other words, space of tangent vectors to $M$ at $x$.
Oct
25
comment $ \lim_{n\rightarrow \infty}n^{-\frac{1}{2}\left(1+\frac{1}{n}\right)}\cdot \left(1^1\cdot 2^2…n^n\right)^{\frac{1}{n^2}}$
Maybe you can still use product of limits although your first limit is wrong. Its simple enough. The second limit in the product can be obtained by using the "sandwich" theorem. Just look at how the term $(1.2^2.3^2 \ldots n^n)^{\frac{1}{n^2}}$ is bounded.
Oct
25
revised Fixed field of two subgroups of $\operatorname{Aut}_{K}{K(x)}$
improved formatting
Oct
25
suggested approved edit on Fixed field of two subgroups of $\operatorname{Aut}_{K}{K(x)}$
Oct
24
accepted Clarification of notion of proper group action.
Oct
24
comment Clarification of notion of proper group action.
Gosh!! I was just suggested the same book by a friend. Thanks a lot. Just one clarification. Why the big fuss about moving compact sets and not any other kind??Does bringing in compactness facilitate anything??Thanks again!!
Oct
23
asked Clarification of notion of proper group action.
Oct
22
comment Linear Algebra Subspace question
As Matt said, you seem to have confused the vectors with the components $b_1, b_2, b_3$. All you need to do is just go through the terms and definitions governing this problem, you will be done. I suggest you try and do it yourself.