Invariants of Homology 3-Spheres

2002
ISBN: 978-3-540-43796-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 140, 223 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1140 g

Reihe: Encyclopaedia of Mathematical Sciences

Homology 3-sphere is a closed 3-dimensional manifold whose homology equals that of the 3-sphere. These objects may look rather special but they have played an outstanding role in geometric topology for the past fifty years. The book gives a systematic exposition of diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered are constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, including invariants of Walker and Lescop, Herald and Lin invariants of knots, and equivariant Casson invariants, Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. It will be appealing to both graduate students and researchers in mathematics and theoretical physics.

Zielgruppe

Research

Autoren/Hrsg.

Saveliev, Nikolai

Vassiiev, A.

Gamkrelidze, R.V.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

1 Homology 3-Spheres.- 2 Rokhlin Invariant.- 3 Casson Invariant.- 4 Invariants of Walker and Lescop.- 5 Casson Invariant and Gauge Theory.- 6 Instanton Floer Homology.- 7 The Homology Cobordism Group.- References.