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Apr
15
answered Symplectic positive definite matrix.
Apr
14
comment Embedding/Submersion Properties of Cotangent Maps (Pullbacks)
Yes, $d\phi$ (or $\phi_\ast$, or $T\phi$) is the differential of $\phi$. I think (4) should be true as well, since $\phi$ will be a diffeomorphism on the total spaces and it is linear on the fibers.
Apr
14
answered Embedding/Submersion Properties of Cotangent Maps (Pullbacks)
Apr
13
comment Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
Updated to include a sketch of the proof. You can find the details in the lecture notes by Cannas da Silva.
Apr
13
revised Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
added 1002 characters in body
Apr
13
answered formal glueing of schemes
Apr
12
comment Exactness Axiom of Homology Theory
$C_k(\cdot)$ are the chains, with boundary map $\partial: C_k(\cdot) \to C_{k-1}(\cdot)$, so that $H_k = \ker \partial_k / \mathrm{im} \partial_{k+1}$. They depend on what homology theory you are considering, but they are always there in the background somewhere. For the singular homology of a space $X$ they are formal linear combinations of maps $\Delta^k \to X$ where $\Delta^k$ is the standard $k$-simplex. For simplicial and cellular homology there are analogous definitions. Whenever you encounter any kind of homology you should think of it as the homology of some underlying chain complex.
Apr
9
answered subgroup problem in abstract algebra
Apr
8
comment Center of Clifford Algebra depending on the parity of $\dim V$?
The parity issue is discussed in detail in E. Meinrenken's Notes math.toronto.edu/mein/teaching/clif_main.pdf . See Proposition 2.6 in particular, which gives the result over $\mathbb{C}$. Another good reference is Chevalley's book.
Apr
8
revised Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
small commment added
Apr
8
answered Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
Apr
7
answered Exactness Axiom of Homology Theory
Mar
16
answered Structure Sheaf on Scheme
Feb
13
answered Fourier transform of gaussian times polynomial to a high power
Feb
9
comment Non-closed subgroups of Lie groups
Irrational flows on the torus are well-studied (and famous) examples in noncommutative geometry. So it might be worth looking at the noncommutative geometry literature to see if there is anything like what you're asking.
Feb
4
comment Expressing Differential Form in Different Coordinates
@Confused I edited it to include a few more details of the evaluation of the pushforward.
Feb
4
awarded  Editor
Feb
4
revised Expressing Differential Form in Different Coordinates
added some extra detail
Feb
2
answered Expressing Differential Form in Different Coordinates
Nov
25
awarded  Nice Answer