Lectures on the topology of 3-manifolds : an introduction to the Casson invariant /

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Bibliographic Details
Author / Creator:	Saveliev, Nikolai, 1966-
Imprint:	Berlin ; New York : Walter de Gruyter, 1999.
Description:	1 online resource (ix, 199 pages) : illustrations
Language:	English
Series:	De Gruyter textbook De Gruyter textbook.
Subject:	Three-manifolds (Topology) Three-manifolds (Topology) Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11382690

Hidden Bibliographic Details
ISBN:	9783110806359 3110806355 3110162725 9783110162721 3110162717 9783110162714
Digital file characteristics:	data file
Notes:	Includes bibliographical references (pages 186-195) and index. Print version record.
Summary:	"Progress in low-dimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his [lambda]-invariant. The purpose of this book is to provide a much-needed bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and gives a brief sketch of links with the latest developments in low-dimensional topology and gauge theory." "The text will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincare duality on manifolds."--Jacket.
Other form:	Print version: Saveliev, Nikolai, 1966- Lectures on the topology of 3-manifolds 3110162725

Table of Contents:

Preface
Introduction
Glossary
1 Heegaard Splittings
1.1 Introduction
1.2 Existence Of Heegaard Splittings
1.3 Stable Equivalence Of Heegaard Splittings
1.4 The Mapping Class Group
1.5 Manifolds Of Heegaard Genus â?? 1
1.6 Seifert Manifolds
2 Dehn Surgery
2.1 Knots And Links In 3-Manifolds
2.2 Surgery On Links In S3
2.3 Surgery Description Of Lens Spaces And Seifert Manifolds
2.4 Surgery And 4-Manifolds
3 Kirby Calculus
3.1 The Linking Number
3.2 Kirby Moves
3.3 The Linking Matrix
3.4 Reversing Orientation 4 Even Surgeries
5 Review Of 4-Manifolds
5.1 Definition Of The Intersection Form
5.2 The Unimodular Integral Forms
5.3 Four-Manifolds And Intersection Forms
6 Four-Manifolds With Boundary
6.1 The Intersection Form
6.2 Homology Spheres Via Surgery On Knots
6.3 Seifert Homology Spheres
6.4 The Rohlin Invariant
7 Invariants Of Knots And Links
7.1 Seifert Surfaces
7.2 Seifert Matrices
7.3 The Alexander Polynomial
7.4 Other Invariants From Seifert Surfaces
7.5 Knots In Homology Spheres 7.6 Boundary Links And The Alexander Polynomial
8 Fibered Knots
8.1 The Definition Of A Fibered Knot
8.2 The Monodromy
8.3 More About Torus Knots
8.4 Joins
8.5 The Monodromy Of Torus Knots
9 The Arf-Invariant
9.1 The Arf-Invariant Of A Quadratic Form
9.2 The Arf-Invariant Of A Knot
10 Rohlinâ€?S Theorem
10.1 Characteristic Surfaces
10.2 The Definition Of QÌ?
10.3 Representing Homology Classes By Surfaces
11 The Rohlin Invariant
11.1 Definition Of The Rohlin Invariant 11.2 The Rohlin Invariant Of Seifert Spheres
11.3 A Surgery Formula For The Rohlin Invariant
11.4 The Homology Cobordism Group
12 The Casson Invariant
13 The Group Su(2)
14 Representation Spaces
14.1 The Topology Of Representation Spaces
14.2 Irreducible Representations
14.3 Representations Of Free Groups
14.4 Representations Of Surface Groups
14.5 Representations Of Seifert Homology Spheres
15 The Local Properties Of Representation Spaces
16 Cassonâ€?S Invariant For Heegaard Splittings 16.1 The Intersection Product
16.2 The Orientations
16.3 Independence Of Heegaard Splitting
17 Cassonâ€?S Invariant For Knots
17.1 Preferred Heegaard Splittings
17.2 The Casson Invariant For Knots
17.3 The Difference Cycle
17.4 The Casson Invariant For Unlinks
17.5 The Casson Invariant Of A Trefoil
18 An Application Of The Casson Invariant
18.1 Triangulating 4-Manifolds
18.2 Higher-Dimensional Manifolds
19 The Casson Invariant Of Seifert Manifolds

Lectures on the topology of 3-manifolds : an introduction to the Casson invariant /

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