Cluster algebras and triangulated surfaces. Part I: Cluster complexes
- S. Fomin, M. Shapiro, D. Thurston
- Mathematics
- 15 August 2006
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 algebra…
On combinatorial link Floer homology
- Ciprian Manolescu, P. Ozsváth, Z. Szabó, D. Thurston
- Mathematics
- 18 October 2006
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 2…
Characterizing generic global rigidity
- S. Gortler, Alexander Healy, D. Thurston
- Mathematics
- 4 October 2007
Legendrian knots, transverse knots and combinatorial Floer homology
- P. Ozsváth, Z. Szabó, D. Thurston
- Mathematics
- 27 November 2006
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 also…
Integral Expressions for the Vassiliev Knot Invariants
- D. Thurston
- Mathematics
- 25 January 1999
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,…
Bordered Heegaard Floer homology
- Robert Lipshitz, P. Ozsváth, D. Thurston
- MathematicsMemoirs of the American Mathematical Society
- 3 October 2008
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 with…
Bimodules in bordered Heegaard Floer homology
- Robert Lipshitz, P. Ozsváth, D. Thurston
- Mathematics
- 2 March 2010
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 this…
Perturbative 3-manifold invariants by cut-and-paste topology
- G. Kuperberg, D. Thurston
- Mathematics
- 21 December 1999
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 field…
The Århus integral of rational homology 3-spheres II: Invariance and universality
- D. Bar-Natan, S. Garoufalidis, L. Rozansky, D. Thurston
- Mathematics
- 11 January 1998
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 integral…
Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths
- S. Fomin, D. Thurston
- MathematicsMemoirs of the American Mathematical Society
- 20 October 2012
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 Teichmueller…
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