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Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Penned By S. Cappell
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Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Penned By S. Cappell
4.85 83,420 Ratings
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Editor's Note:
Many phenomena of three-manifolds are related to the representations of their fundamental groups. The authors of this book, using an investigation of the intersections of Lagrangian subvarieties in singular symplectic varieties, develop invariants associated with the more general Lie group, including SU(n). From a combinatorial approach related to Vassiliev's perspective on knot theory, a number of researchers have obtained a theory of "finite-type invariants" of three-manifolds. The authors show that their general representation-theoretic invariants are of the finite type. As a result, their invariants have surgery formulae and are intimately related to issues in mapping class groups, knot theory and quantum physics. On the other hand, some combinatorial invariants are given new geometrical meaning through these relations with the fundamental group.

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Length 200 Pages
Released October 1, 1999
Identifier (ISBN) 2498534
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S. Cappell
The Mind Behind the Work
S. Cappell

After spending years working in the corporate world, S. Cappell finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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