1
vote
0answers
92 views
Topological classification of a real-valued functions on manifold
What is a motivation to study topological conjugacy of a real-valued functions on a manifold? (The importance of notion of a topologically conjugate homeomorphisms is clear for me) …
1
vote
3answers
219 views
Linearization of vector fields
Simply, we discuss things on $C^{2n}$ ($or R^{2n}$) but not on manifolds. Given an anayltic (or real analytic) vector field $V$ on $C^{2n}$ ($or R^{2n}$), with a zero at the origin …
0
votes
0answers
147 views
Clifford algebra on almost product structure
Is the algebra defined by $J^2=1$,i.e. (algebra defined on almost product structure ) Clifford algebra?
1
vote
1answer
147 views
Thom-Gysin Sequences and Stratifications
Let $X$ be an affine algebraic variety over $\mathbb{C}$, and let $G$ be a semisimple complex linear algebraic group acting by variety automorphisms with finitely many orbits. The …
4
votes
1answer
164 views
A regular polytope
For positive integers $m$ and $n$, consider a regular polytope in ${\mathbb R}^{m+n+mn}$ with $2^{m+n}$ vertices, corresponding to each $\sigma \in \{-1,1\}^{m+n}$ as follows. Th …
8
votes
3answers
648 views
Intuition for Levi-Civita connection via Hamiltonian flows
A Euclidean metric on a manifold $X$ defines a function on the symplectic space $T^*X$ whose Hamiltonian flow gives geodesics. Is there a similar interpretation of the Levi-Civita …
0
votes
2answers
149 views
Lagrangian submanifolds
Let $\Lambda_{n}$ be the set of all Lagrangian subspaces of $C^{n}$, and $P\in\Lambda_{n}$. Put $U_{P}= ( Q\in\Lambda_{n} : Q\cap (iP)=0 )$. There is an assertion that the set $U_{ …
1
vote
1answer
126 views
A basic question related to Hamiltonian isotopy in symplectic geometry
In any standard symplectic geometry/topology textbook, the concept of Hamiltonian isotopy was introduced:
$(M, \omega)$ is a sympplectic manifold. Given a symplectic isotopy
$\phi …
3
votes
1answer
130 views
Trivial canonical bundle of a Ricci-flat, simplyconnected Kähler manifold
Hallo,
I have two questions where I do not really know how to deal with them. Let $(M,J,g)$ be a Kähler manifold, where $g$ is the Riemannian metric and denote by $\omega(\cdot , …
7
votes
1answer
174 views
quasi conformal, area preserving homomorphisms of the disc
Restricting a quasi-conformal homeomorphism of the disc to the boundary gives a surjective homomorphism from $QC(D^2)$ (quasi-conformal homeos of $D^2$) to $QS(S^1)$ (quasi-symmetr …
7
votes
1answer
333 views
Darboux like theorem for non-degenerate 3-forms in 6-manifolds
we know Darboux theorem for higher-symplectic geometry is not correct in general,
but is there any Darboux like theorem for non-degenerate 3-forms in 6-manifolds?
4
votes
1answer
295 views
conservation law and generalized Symplectic Monge-Ampere equation arising from 3-variables
If we have a Jacobi PDE system with conservation law $\theta \in \Omega^1(M)$ such that $d \theta$ is non-degenerate 2-form , then we know this fact that it can be written as sympl …
0
votes
0answers
112 views
SLAGs on elliptic curves are only lines?
Let $E=\mathbb{C}/(\mathbb{Z}+\tau\mathbb{Z})$ be an alliptic curve. Define a holomorphic 1-form $dz=dx+idy$ and a Kahler form $\omega=dx\wedge dy$. How can one prove that special …
1
vote
1answer
123 views
Torsion-free $G$-Structures
I have the following question. Let $G \subset SO(n)$ be a Lie Group and $M$ be a smooth manifold of dimension $n$. Furthermore let $P$ be a $G$-structure on $M$ i.e. $P$ is a princ …
5
votes
0answers
187 views
What is known about the strong Arnold conjecture?
Here are the two versions of Arnold's conjecture on Hamiltonian orbits:
Let $(M,\omega)$ be a closed symplectic manifold, and let $H: \mathbb{R/Z} \times M \to \mathbb{R}$ be a …

