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Lectures on the Topology Of 3-Manifolds : An Introduction to the Casson Invariant.

By: Series: De Gruyter Textbook SerPublisher: Berlin/Boston : De Gruyter, Inc., 1999Copyright date: ©1999Description: 1 online resource (208 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110806359
Subject(s): Genre/Form: Additional physical formats: Print version:: Lectures on the Topology Of 3-Manifolds : An Introduction to the Casson InvariantDDC classification:
  • 514/.34
LOC classification:
  • QA613.2.S28 1999eb
Online resources:
Contents:
Intro -- 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 ≤ 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 Rohlin'S Theorem -- 10.1 Characteristic Surfaces -- 10.2 The Definition Of Q̃ -- 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 Casson'S Invariant For Heegaard Splittings -- 16.1 The Intersection Product -- 16.2 The Orientations -- 16.3 Independence Of Heegaard Splitting -- 17 Casson'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 -- 19.1 The Space R(P, Q, R) -- 19.2 Calculation Of The Casson Invariant -- Conclusion -- Exercises -- Bibliography -- Index.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF-N00019797
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP-N00019797
Ebrary Ebrary Sudan Available
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Total holds: 0

Intro -- 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 ≤ 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 Rohlin'S Theorem -- 10.1 Characteristic Surfaces -- 10.2 The Definition Of Q̃ -- 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 Casson'S Invariant For Heegaard Splittings -- 16.1 The Intersection Product -- 16.2 The Orientations -- 16.3 Independence Of Heegaard Splitting -- 17 Casson'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 -- 19.1 The Space R(P, Q, R) -- 19.2 Calculation Of The Casson Invariant -- Conclusion -- Exercises -- Bibliography -- Index.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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