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olivier dot begassat dot cours at gmail dot com


Jul
15
comment Homotopy limits
I guessed {\em ...} stood for emphasis, please correct if I misinterpreted you.
Jul
15
revised Homotopy limits
deleted 4 characters in body
Jul
3
answered Is the Reversion map in Geometric Algebra well-defined?
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
29
comment Linear Algebra without Matrices
Matrices allow you to make calculations mechanical, and to state results concisely. There are definite instances where matrices save you times and ink.
Jun
27
comment Topologies on n-manifolds
Do you mean wether it is useful of even necessary to study general topology before learning about manifolds? I don't think so, at least if you are well acquainted with calculus and euclidean space. But you should know a little about compactness, and probably about covering space theory at some point.
Jun
27
comment Exact Sequences of R-Modules
This question is missing a lot of context. What are the maps? What is $E$?
Jun
26
revised Interpretation of $p$-forms
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Jun
26
comment Existence of $p \times p $ matrices $A$ and $B$ over the field $\mathbb F_p$, $p$ prime, such that $AB-BA=I$.
A related question math.stackexchange.com/questions/125219/… The answer is YES, but I don't know the proof, and it's not straightforward (at least the original proof isn't).
Jun
26
revised Interpretation of $p$-forms
added 75 characters in body
Jun
26
answered Interpretation of $p$-forms
Jun
25
comment Canonical orientation of a complex manifold
The orientation is different for even $n$. The second choice may have the added advantage that the transition matrices are bloc matrices with blocs of the form $$\begin{pmatrix} a&-b\\b&a\end{pmatrix}$$ and so identifies nicely with complex $n\times n$ matrices.
Jun
24
reviewed Reject suggested edit on $\pi_1 (x,y) = x$ the projection function with $\pi_1 : R^2 \rightarrow R$
Jun
24
reviewed Approve suggested edit on Expected revenue obtained by the Vickery auction with reserve price $1/2$
Jun
23
revised $SL(V)$ and $PSL(V)$ act $k$-transitively on the space of all $1$-dimensional subspaces.
deleted 58 characters in body
Jun
23
answered $SL(V)$ and $PSL(V)$ act $k$-transitively on the space of all $1$-dimensional subspaces.
Jun
23
comment Show $\mathbb{CP^2/CP^1}$ is not a retract of $\mathbb{CP^4/CP^1}$.
$\Bbb CP^2/\Bbb CP^1$ is homeomorphic to the $4$ sphere, and thus its cohomology ring is $\Bbb Z[t]/(t^2)$ with $t$ of degree $4$. If you use the long exact cohomology sequence $$\cdots\to \tilde{H}^*(\Bbb CP^4/\Bbb CP^1)\to H^*(\Bbb CP^4)\to H^*(\Bbb CP^1)\to \cdots$$ you can see that the cohomology ring of $\Bbb CP^4/\Bbb CP^1$ is $\Bbb Z[u,v]/(u^3,v^2,uv=vu=0)$ with $u$ in degree $4$ and $v$ in degree $6$. I'm not certain you can solve the problem only using the ring structure of cohomology.
Jun
23
comment Show $\cos\theta=\frac12(\text{tr}(g)-1)$ with $g\in\text{SO}(3)$
@amWhy upon looking very carefully I did indeed see this ^^ all joking aside, I don't understand the question, but it's fine if all doubts were cleared up by your answer.
Jun
23
comment Show $\cos\theta=\frac12(\text{tr}(g)-1)$ with $g\in\text{SO}(3)$
@amWhy I don't understand what is holding OP back from dividing the equality $\mathrm{tr}(g)-1=2\cos(\theta)$ by $2$...