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Cluster Algebras and Poisson Geometry
About this Title
Michael Gekhtman, University of Notre Dame, Notre Dame, IN, Michael Shapiro, Michigan State University, East Lansing, MI and Alek Vainshtein, University of Haifa, Haifa, Mount Carmel, Israel
Publication: Mathematical Surveys and Monographs
Publication Year:
2010; Volume 167
ISBNs: 978-0-8218-4972-9 (print); 978-1-4704-1394-1 (online)
DOI: https://doi.org/10.1090/surv/167
MathSciNet review: MR2683456
MSC: Primary 13F60; Secondary 37K20, 37K25, 53D17
Table of Contents
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Front/Back Matter
Chapters
- 1. Preliminaries
- 2. Basic examples: Rings of functions on Schubert varieties
- 3. Cluster algebras
- 4. Poisson structures compatible with the cluster algebra structure
- 5. The cluster manifold
- 6. Pre-symplectic structures compatible with the cluster algebra structure
- 7. On the properties of the exchange graph
- 8. Perfect planar networks in a disk and Grassmannians
- 9. Perfect planar networks in an annulus and rational loops in Grassmannians
- 10. Generalized Bäcklund-Darboux transforms for Coxeter-Toda flows from a cluster algebra perspective