• Corpus ID: 119235773

Orientations of Morse flow trees in Legendrian contact homology

@article{Karlsson2015OrientationsOM,
  title={Orientations of Morse flow trees in Legendrian contact homology},
  author={Cecilia Karlsson},
  journal={arXiv: Symplectic Geometry},
  year={2015}
}
Let L be a spin Legendrian submanifold of the 1-jet space of a smooth manifold. We prove that the Legendrian contact homology of L with integer coefficients can be computed using Morse flow trees. We also give an algorithm for explicitly computing the sign of a rigid flow tree. 
View PDF on arXiv
7 Citations
Background Citations
1
Methods Citations
2

7 Citations

On the compactification of bounded edge Morse flow trees

Let L ⊂ J 1 ( M ) be a closed Legendrian submanifold of the 1-jet space of a closed Riemannian manifold ( M, g ) and consider the moduli space L ( N ) of Morse flow trees in L with at most N edges and…

A note on coherent orientations

Let L R J .M/ be a spin, exact Lagrangian cobordism in the symplectization of the 1-jet space of a smooth manifold M . Assume that L has cylindrical Legendrian ends ƒ ̇ J .M/. It is well known that…

Augmented Legendrian cobordism in $J^1S^1$

We consider Legendrian links and tangles in JS and J[0, 1] equipped with Morse complex families over a field F and classify them up to Legendrian cobordism. When the coefficient field is F2 this…

Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds

Let $\Lambda$ be a link of Legendrian spheres in the boundary of a subcritical Weinstein manifold $X$. We show that the computation of the Legendrian contact homology of $\Lambda$ can be reduced to a…

Koszul duality via suspending Lefschetz fibrations

  • Yin Li
  • Mathematics
    Journal of Topology
  • 2019
Let M be a Liouville 6‐manifold which is the smooth fiber of a Lefschetz fibration on C4 constructed by suspending a Lefschetz fibration on C3 . We prove that for many examples including…

A note on coherent orientations for exact Lagrangian cobordisms

Let $L \subset \mathbb R \times J^1(M)$ be a spin, exact Lagrangian cobordism in the symplectization of the 1-jet space of a smooth manifold $M$. Assume that $L$ has cylindrical Legendrian ends…

Braid loops with infinite monodromy on the Legendrian contact DGA

We present the first examples of elements in the fundamental group of the space of Legendrian links in (S, ξst) whose action on the Legendrian contact DGA is of infinite order. This allows us to…

References

SHOWING 1-10 OF 39 REFERENCES

Knot contact homology

The conormal lift of a link K in ℝ3 is a Legendrian submanifold ΛK in the unit cotangent bundle U∗ℝ3 of ℝ3 with contact structure equal to the kernel of the Liouville form. Knot contact homology, a…

Floer homology of Lagrangians in clean intersection

We consider Floer homology associated to a pair of closed Lagrangian submanifolds that satisfy a monotonicty assumption. If the Lagrangians intersect cleanly we decribe two spectral sequences which…

Legendrian Contact Homology

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P × R where P is an exact symplectic manifold is established. The class of such contact…

Symplectic homology product via Legendrian surgery

TLDR
The product and Batalin–Vilkovisky operator of symplectic homology is expressed in terms of the Legendrian homology algebra of the attaching spheres of critical handles in that context.

Knotted Legendrian surfaces with few Reeb chords

For g > 0, we construct g + 1 Legendrian embeddings of a surface of genus g into J(1)(R-2) = R-5 which lie in pairwise distinct Legendrian isotopy classes and which all have g + 1 transverse Ree ...

Legendrian Contact Homology in P X R

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $P\times \R$ where $P$ is an exact symplectic manifold is established. The class of such…

Orientations for pseudoholomorphic quilts

We construct coherent orientations on moduli spaces of pseudoholomorphic quilts and determine the effect of various gluing operations on the orientations. We also investigate the behavior of the…

Legendrian contact homology in $P \times \mathbb{R}$

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P x R, where P is an exact symplectic manifold, is established. The class of such contact…

A complete knot invariant from contact homology

We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely…

Knot and braid invariants from contact homology II

We present a topological interpretation of knot and braid contact homology in degree zero, in terms of cords and skein relations. This interpretation allows us to extend the knot invariant to…