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Cluster algebras and triangulated surfaces. Part I: Cluster complexes
We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such a cluster algebraExpand
On combinatorial link Floer homology
Link Floer homology is an invariant for links defined using a suitable version of Lagrangian Floer homology. In an earlier paper, this invariant was given a combinatorial description with mod 2Expand
Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths
For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated TeichmuellerExpand
Integral Expressions for the Vassiliev Knot Invariants
It has been folklore for several years in the knot theory community that certain integrals on configuration space, originally motivated by perturbation theory for the Chern-Simons field theory,Expand
The Århus integral of rational homology 3-spheres II: Invariance and universality
Abstract. We continue the work started in [Å-I], and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Århus integralExpand
Naturality and Mapping Class Groups in Heegaard Floer Homology
We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, andExpand
Bordered Heegaard Floer homology
We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold withExpand
Legendrian knots, transverse knots and combinatorial Floer homology
Using the combinatorial approach to knot Floer homology, we define an invariant for Legendrian knots in the three-sphere, which takes values in link Floer homology. This invariant can be used to alsoExpand
Bimodules in bordered Heegaard Floer homology
Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A(F) and to a three-manifold Y with boundary identified with F a module over A(F). In thisExpand
Perturbative 3-manifold invariants by cut-and-paste topology
Author(s): Kuperberg, Greg; Thurston, Dylan P. | Abstract: We give a purely topological definition of the perturbative quantum invariants of links and 3-manifolds associated with Chern-Simons fieldExpand