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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… Expand

On combinatorial link Floer homology

- Ciprian Manolescu, P. Ozsvath, 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… Expand

Cluster Algebras and Triangulated Surfaces
Part II: Lambda Lengths

- S. Fomin, D. Thurston
- Mathematics
- Memoirs of the American Mathematical…
- 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… Expand

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,… Expand

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… Expand

Naturality and Mapping Class Groups in Heegaard Floer Homology

- Andr'as Juh'asz, D. Thurston, Ian Zemke
- Mathematics
- Memoirs of the American Mathematical Society
- 18 October 2012

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, and… Expand

Bordered Heegaard Floer homology

- R. Lipshitz, P. Ozsvath, D. Thurston
- Mathematics
- Memoirs of the American Mathematical…
- 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… Expand

Legendrian knots, transverse knots and combinatorial Floer homology

- P. Ozsvath, 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… Expand

Bimodules in bordered Heegaard Floer homology

- R. Lipshitz, P. Ozsvath, 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… Expand

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… Expand

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