Contact cuts

By Eugene Lerman. 2000

50 citations recorded by the source corpus.

We describe a contact analog of the symplectic cut construction [L]. As an application we show that the group of contactomorphisms for certain overtwisted contact structures on lens spaces contains countably many non-conjugate two tori.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/263fca1bf371b353cbfc39e657485b33be3f7c8a

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Contact Toric Manifolds (2001, methodology): “e that t 2 −t 1 6= πn, n= 1,2,..., for otherwise µ 1 = ±µ 2 and then B/∼ is S2 ×S1 6= RP3. Next observe that since the standard contact structure on S∗S2 = Mis tight, we must have t 2 − t 1 <π(cf. [L2]). Indeed, if t 1 = 0 and t 2 >π, the image of the cylinder {(1,eiθ,t) | 0 ≤ t≤ t 2,θ∈ R} ⊂ B”
The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits (2006, background): “An infinite number of conjugacy classes of maximal tori has already been encountered in the case of some groups of contactomorphisms (see [20]).”
Weak and strong fillability of higher dimensional contact manifolds (2011, methodology): “This process is equivalent to performing a contact cut of V with respect to the (local) θ -action, as described in [40].”