Electronic catalog

DDC 514.34
S 26
Saveliev, Nikolai.
    Lectures on the Topology of 3-Manifolds [[electronic resource] :] : an Introduction to the Casson Invariant. / Nikolai. Saveliev. - 2nd ed. - Berlin : : De Gruyter,, 2011. - 1 online resource (219 p.). - URL: https://library.dvfu.ru/lib/document/SK_ELIB/AD425ADF-8232-4F7D-903F-E27343AD6B01 . - ISBN 9783110250367 (electronic bk.). - ISBN 3110250365 (e lectronic bk.)
Description based on print version record.
Параллельные издания: Print version: : Saveliev, Nikolai Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant. - Berlin : De Gruyter, c2011. - ISBN 9783110250350
    Содержание:
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; 1.7 Heegaard diagrams; 1.8 Exercises; 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; 2.5 Exercises; 3 Kirby calculus; 3.1 The linking number; 3.2 Kirby moves; 3.3 The linking matrix; 3.4 Reversing orientation; 3.5 Exercises.
4 Even surgeries4.1 Exercises; 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; 5.4 Exercises; 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; 6.5 Exercises; 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.
7.7 Exercises8 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; 8.6 Open book decompositions; 8.7 Exercises; 9 The Arf-invariant; 9.1 The Arf-invariant of a quadratic form; 9.2 The Arf-invariant of a knot; 9.3 Exercises; 10 Rohlin's theorem; 10.1 Characteristic surfaces; 10.2 The definition of q~; 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 invariant11.4 The homology cobordism group; 11.5 Exercises; 12 The Casson invariant; 12.1 Exercises; 13 The group SU (2); 13.1 Exercises; 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 for Seifert homology spheres; 14.6 Exercises; 15 The local properties of representation spaces; 15.1 Exercises; 16 Casson's invariant for Heegaard splittings; 16.1 The intersection product; 16.2 The orientations.
16.3 Independence of Heegaard splitting16.4 Exercises; 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 boundary links; 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; 18.3 Exercises; 19 The Casson invariant of Seifert manifolds; 19.1 The space R(S (p, q, r)); 19.2 Calculation of the Casson invariant; 19.3 Exercises; Conclusion; Bibliography; Index.

Saveliev, Nikolai. Lectures on the Topology of 3-Manifolds [[electronic resource] :] : an Introduction to the Casson Invariant. / Nikolai. Saveliev, 2011. - 1 online resource (219 p.) с. (Введено оглавление)