bio | website | |
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location | Silesia, Czech Republic | |
age | 36 | |
visits | member for | 2 years, 10 months |
seen | yesterday | |
stats | profile views | 622 |
Reasonably expert in Differential Geometry, I work mostly with jet bundles and their natural structures trying to exploit them in the areas of nonlinear PDEs and Calculus of Variations.
Oct 23 |
revised |
Extending derivations to the superposition closure
added 787 characters in body |
Oct 7 |
revised |
Extending derivations to the superposition closure
added 3 characters in body |
Oct 7 |
asked | Extending derivations to the superposition closure |
Oct 4 |
accepted | How to “lift” a transitive group action on a manifold? |
Sep 30 |
comment |
How to “lift” a transitive group action on a manifold?
@BenMcKay: incidentally, can you always realise $\frak{g}$, the Lie algebra of $G$, as an algebra of vector fields on $M$, i.e., can you embed it into the (infinite-dimensional) Lie algebra of vector fields on $M$? |
Sep 30 |
comment |
How to “lift” a transitive group action on a manifold?
@VítTuček: yes, actually in the cases I'm interested in, $\widetilde{M}$ is compact. |
Sep 29 |
comment |
How to “lift” a transitive group action on a manifold?
Indeed. This is more or less what I suggested in my last lines. I'm aware of Lie-Palais theorem, though you need to require some extra topological conditions from $\widetilde{M}$. Still, I'd like to see some universal property characterising $\widetilde{G}$, like, e.g., "it is the unique group admitting $G$ as a factor by covering transformations", or something like that, and/or some algebraic way to construct it out of the available data! |
Sep 29 |
asked | How to “lift” a transitive group action on a manifold? |
Sep 29 |
comment |
What is the most useful non-existing object of your field?
As a general rule, you appoint a name to something if that thing has been around for a while: even if its existence is disproved later, the name will stick to it. It's a nice phenomenon. Think about the aether: for decades people believed it surrounded us, now we know it cannot exists, but its name persists in SF and fantasy tales! I guess that before Galois the name "general solution for quintic equations" was often used, both by those who believed it existed and it was yet to be found, by those who erroneously believed they found it, and by those who were trying to prove it cannot exists! |
Sep 24 |
awarded | Autobiographer |
Sep 9 |
accepted | Can the finiteness of a Burnside group with two generators be checked algorithmically by using Fuchsian von Dyck groups? |
Sep 8 |
comment |
Can the finiteness of a Burnside group with two generators be checked algorithmically by using Fuchsian von Dyck groups?
Your almost cleared out all my doubts - yet I need time to fully digest your answer. Now, let us focus on your last sentence: "I certainly don't see any particular obstruction to attempting the computation in the case of $B(2,5)$". Believe me, I've been trying for years to find out what is the state-of-the-art concerning the finiteness of $B(2,5)$, but in vain. Can you point out somebody to whom I may ask? Why there are a lot of computers employed to discover the 'last' digit of $\pi$, or the 'biggest' prime, but none cares about finiteness of $B(2,5)$? Is there at least the algorithm written? |
Sep 5 |
revised |
Can the finiteness of a Burnside group with two generators be checked algorithmically by using Fuchsian von Dyck groups?
Previous question, titled "Coverings of the free Burnside groups", was never answered. So, I reformulate it adding new details I discovered meanwhile. |
Aug 6 |
accepted | Is there a “unique” homogeneous contact structure on odd-dimensional spheres? |
Jul 16 |
comment |
Symmetry analysis of differential equations
The standard reference on this concern is Michor's book mat.univie.ac.at/~michor/… Anyway, I would guess that there are only two homotopy types: the orientation-preserving and the orientation-reversing. The identical transformation is the diagonal of $\mathbb{R}^2$, and I don't see any reason why it shouldn't be possible to deform the graph of any other orientation-preserving transformation to the diagonal. |
Jul 11 |
comment |
Euler Class of a vector field
@HenryT.Horton: why do you need to pass to a 2-plane field? Besides, in the question there are no metrics mentioned, so you cannot take "orthogonal"... What about the line bundle spanned by $X$? I think in this case, the Euler class just tells whether $X$ is nowhere vanishing or not (e.g., if I'm not mistaken, on the 2-sphere all fields should have nonzero Euler class). |
Jul 9 |
answered | Generalized Leibniz rule |
Jul 7 |
awarded | Nice Question |
Jul 4 |
comment |
Is there a “unique” homogeneous contact structure on odd-dimensional spheres?
@RobertBryant : following your comment, I added a long edit to the original question. |
Jul 4 |
revised |
Is there a “unique” homogeneous contact structure on odd-dimensional spheres?
Added a long edit following R. Bryant's last remark. |