The study of topological invariants of contact manifolds, the odd-dimensional counterpart of symplectic manifolds. Classical mechanics has a 2n-dimensional phase space and one time dimension and the definition of contact manifolds axiomatizes this structure by positing a maximally non-integrable hyperplane distribution. Fields of application include low-dimensional topology, 3-manifolds and knots, geometrical optics, thermodynamics and control theory.
Questions tagged [contact-topology]
93 questions
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closed orbits in the flow of the Reeb vector field of a contact manifold
This is once again from Hansjorg Geiges' introduction to contact topology. In Gray Stability Theorem in $\S2.2$ asserts that one can achieve stability of contact structures. However, one can't in general achieve stability of contact forms. An…
Karthik C
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different contact structures
Let $M = B^2_R \times S^1$ where $B^2_R$ is the 2-dimensional open ball with radius $R (>1)$. Take two contact structures $\alpha_1 = \frac{1}{2} (xdy - ydx) + dt$ and $\alpha_2 = \frac{1}{2} (xdy - ydx) + 2 dt$.
Question: is there a diffeomorphism…
user72443
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Motivation of contact topology
I want to ask about motivations of contact topology. I mean, for example, a symplectic manifold is a generalization of phase spaces and it explains why we need a closed, non-degenerate symplectic form.
I feel like a contact manifold also has the…
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