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Mathematics - Geometry & Topology | Surfaces in 4-Space

Surfaces in 4-Space

Carter, Scott, Kamada, Seiichi, Saito, Masahico

2004, XIII, 214 p.

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Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included.

This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case.

As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.

Content Level » Research

Keywords » homology - quandle - rack homology - surfaces - topological invariant

Related subjects » Geometry & Topology

Table of contents 

1 Diagrams of Knotted Surfaces.- 2 Constructions of Knotted Surfaces.- 3 Topological Invariants.- 4 Quandle Cocycle Invariants.- Epilogue.- Append.- References.

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