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arXiv · 2007.07108

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

Cecilia Karlsson
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Abstract

Let $\Lambda$ be a link of Legendrian spheres in the boundary of a subcritical $2n$-dimensional Weinstein manifold $X$. We show that, under some geometrical assumptions, the computation of the Legendrian contact homology of $\Lambda$ can be reduced to a computation of Legendrian contact homology in 1--jet spaces. Since the Legendrian contact homology in 1--jet spaces is well studied, this gives a simplified way to compute the Legendrian contact homology of $\Lambda$. We restrict to the case when the attaching spheres of the subcritical handles of $X$ do not interact with each other, and we assume that there are no handles of index $n-1$. Moreover, we will only consider mod 2 coefficients for now. The more general situation will be addressed in a forthcoming paper. As an application we compute the homology of the free loop space of $\mathbb{CP}^2$.

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Cecilia Karlsson. 2020-07-14. Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds. https://arxiv.org/abs/2007.07108

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