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Questions related from Ali Taghavi
Dear colleagues, I would appreciate if you give comment on my following MO question. In this MO post I tried to introduce a quantity associated to a (finite, Lie or quantum)...
10 June 2025 6,826 2 View
Dear Colleagues About 5 years ago I asked this question in MO. I would appreciate if you give comment on this...
12 July 2024 6,406 14 View
Is there a polynomial Hamiltonian vector field with a finite number of periodic orbits? Please see this MO question:...
22 January 2021 2,074 4 View
I would appreciate if you give comment or answer on the following...
01 March 2019 9,529 0 View
Assume that we have an analytic simple closed curve \gamma in the plane. Is there a polynomial vector field which is tangent to \gamma? I asked this question at MO,...
29 September 2017 6,502 3 View
For what values of n, not equal to 1,3,7, TS^n is diffeomorphic to an open subsets of R^{2n}?
14 June 2017 9,826 5 View
What is an example of a (compact) manifold which does not admit an atlas with all transition function between charts, polynomials? Of course any such example can not be an affine manifold.
10 April 2017 4,307 2 View
Assume that (M,g) is a Riemannian manifold with the following property: For every p in M, all non singular trajectories of the gradient vector field correspond to function d^2(x,p) are...
14 February 2017 10,002 5 View
Motivated by the fact that the group of isometries of compact Riemann surfaces M_g with g》2 is a finite group , the Hurwitz theorem, we ask the following question: Is there an infinite group G...
17 October 2016 1,012 3 View
Assume that Q(x) is a polynomial with integer coefficients. Is there a prime number p such that the equation Q(x)=0 has all its root in the finite field Z/pZ?
17 February 2016 6,363 10 View
Assume that M is a compact manifold with fixed point property. Let N be a compact submanifold of M x M, with dim (N)=dim (M). Assume that $\pi_{1}:N \to M$ is a surjective map, where $\pi_{1}$...
21 December 2015 7,168 4 View
1)Is there an example of a non trivial principal bundle $P(M,G)$ such that the total space admit a foliation which all leaves are diffeomorphic to $M$? 2) Is there an example of a non...
19 November 2015 4,012 12 View
In these two questions we try to find a relation between vector bundle theory and Lie algebras:(Note that we identify a finite dimensional Lie algebra L with R^n or C^n) 1)Assume that $L$ is...
27 August 2015 8,821 5 View
Let V be a 2-dimensional (real or complex) vector space with 2 generators {C,S}. The trigonometric coalgebra structure on V is defined by the commultiplication $\Delta(C)=C\otimes C-S\otimes S$...
01 July 2015 2,244 1 View
Assume that X is a locally compact Hausdorff space. How can the "Lindelof" property of X be interpreted, in algebraic language, for C_{0}(X)? In particular what would be a "Lindelofization" ...
21 June 2015 4,833 5 View
Assume that M is a compact Riemannian manifold and E is the complexification of TM. Let A be the complex C* algebra H0m(E,E) with natural operations. Are there some reference devoted to...
16 June 2015 5,815 2 View
In the context of noncommutative geometry, according to Serre-Swan theorem, a non commutative vector bundle is defined as a finitely generated projective module over a noncommutative C*...
13 June 2015 5,696 3 View
Does every principle fiber bundle have a flat(hence integrable) connection? In particular is there such a connection for Hopf fibration? If yes, what is the precise description of this 2...
10 June 2015 4,698 9 View
For what type of separable C* algebras, there is no any integer n and any nontrivial morphism from A to the Cuntz algebra O_{n}? In the other word for what type of C* algebras, Hom(A, O_{n})...
06 June 2015 635 2 View
We consider CP^{2n+1} with its natural Riemannian metric(The quotient of S^{4n+3} under the natural action of S^{1}. We denote by "d" the metric which is induced by this Riemannan metric. We...
26 May 2015 2,449 17 View
Assume that a Lie group G acts on a manifold M, effectively. So the Lie algebra g of G is embedded in $\chi^{\infty}(M)$ in a natural way. (effective action: if x.g=x for all x then...
11 May 2015 1,135 3 View
Note that a k- mean on a topological space $X$ is a continuous function $f:X^{k}\to X$ which is identity on the diagonal and is invariant under permutations. In the literature is there an...
21 April 2015 750 2 View
We consider M_{2}(C) as a 8 dimensional manifold with a natural Riemannian metric. The space of projections in M_{2}(C), all A with A=A*=A^{2}, is a two dimensional submanifold homeomorphic to...
14 April 2015 4,361 7 View
What is an example of a simple $C^{*}$ algebra which is acted by $\mathbb{Z}$ but this action can not be extended to an $\mathbb{R}$-action?\Are there such examples for compact operators as...
11 April 2015 9,906 1 View
What is an explicit formula for a Riemannian metric on R^n such that the restriction of this metric to the unit sphere gives us the standard Euclidean distance $\sqrt \sum (x_{i}-y_{i})^2$ on...
09 April 2015 5,450 29 View
Consider the vander pol equation on the plane. Is there a reimannian metric on $\mathbb{R}^{2}-{0}$ such that the trajectories of the vander pol equation would be geodesics, moreover the curvature...
28 March 2015 8,939 14 View
Let $X$ be a hamiltonian vector field on the plane. Then either has no closed orbit or it has infinite number of closed orbit. Now what can be said about higher dimensional hamiltonian vector...
01 January 1970 4,820 10 View
