Legendrian Contact Homology
Legendrian Contact Homology
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传奇接触同源性
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通讯作者：
M. Sullivan
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作者：
T. Ekholm;John B. Etnyre;M. Sullivan
建立了P × R型切触流形中勒让德子流形的切触同调的严格基础，其中P是正合辛流形.这类接触流形包括光滑流形的1-喷空间。作为一个应用程序，接触的同源性是用来提供（光滑）合痕不变量的子流形的R n，更一般地说，不变量的自我横向浸入到R n限制定期同伦。当n = 3时，该应用是Ng [11，12，13]的新结不变量的扩展和提供接触几何基础的第一步。
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 manifolds include 1-jet spaces of smooth manifolds. As an application, contact homology is used to provide (smooth) isotopy invariants of submanifolds of R n and, more generally, invariants of self transverse immersions into R n up to restricted regular homotopies. When n = 3, this application is the first step in extending and providing a contact geometric underpinning for the new knot invariants of Ng [11, 12, 13].