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olivier dot begassat dot cours at gmail dot com


9h
answered Conservation of bilinear forms and conjugation
10h
comment Conservation of bilinear forms and conjugation
And they are bilinear, not hermitian?
10h
comment Conservation of bilinear forms and conjugation
It might matter: over what field are you working? Over the real numbers this is true because $\omega$ and $\omega$ will have the same matrix in well chosen bases. But in general this may require some properties of the ground field (I'm not sure).
14h
comment Fundamental group of two circles joined by an arc
You should tell us what you've tried, and any conjecture you might have. Also, do you know the fundamental group of the circle, and maybe a theorem that allows you to calculate the fg of a space expressed as the union of two simpler ones?
2d
awarded  Popular Question
Jan
20
comment $\alpha \in \mathbb{C}$ with $[\mathbb{Q}(\alpha) : \mathbb{Q}] = 2^k$ but $\alpha$ inconstructible
But $\zeta_6\cdot\sqrt{2}$ manifestly is constructible with a straight edge and a compass.
Jan
20
comment $S^1$ a p-local complex?
What about the usual reduced homology? $H_*(S^1)\simeq\Bbb Z[1]$ is a copy of the integers in degree $1$.
Jan
20
revised Conceptual doubt in a theorem in Group rings
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Jan
20
answered Conceptual doubt in a theorem in Group rings
Jan
20
comment Laplacian and Hodge Laplacian
The Sobolev space of functions is just the Sobolev space of sections of the trivial line bundle.
Jan
20
comment Laplacian and Hodge Laplacian
I take it the Laplacian you talk about in the beginning is defined for real or complex valued functions, but you can define a Sobolev space of $p$-forms, and more generally, Sobolev spaces of sections of vector bundles.
Jan
20
answered Are $(l^1, \|.\|_2)$, $(l^2, \|.\|_3)$ Banach spaces?
Jan
20
comment Orbits of left-multiplication from $\mathrm{PSL}_2(\mathbb Z)$ on $\mathbb Z^{2\times 2}$
$SL_2$ acts on the left, not $PSL_2$.
Jan
19
comment Prove: $\int_0^1 \frac{\ln x }{x-1} d x=\sum_1^\infty \frac{1}{n^2}$
In case anybody reads this answer, I think it is necessary to say something like for all $u\in(0,1)$ and for all $n\in\Bbb N$, $$\left|1+\frac12u+\frac13u^2+\cdots\frac1nu^{n-1}\right|\leq-\frac{\ln(1-u)}u=g‌​(u)$$ so that, since $g$ is integrable on $(0,1)$, one can apply dominated convergence, and swap the sum with the integral.
Jan
19
comment Prove $F^2_{n+1} - F_nF_{n+2} = (-1)^n$
AlexR is correct!
Jan
19
revised Quotient space of $S^n$ and the projective plane
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Jan
19
comment Quotient space of $S^n$ and the projective plane
I doubt it: I don't thinkthe mapping cylinder is orientable when $n$ is even.
Jan
19
revised Quotient space of $S^n$ and the projective plane
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Jan
19
answered Quotient space of $S^n$ and the projective plane
Jan
19
revised Mapping torus with homotopic homeomorphisms
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