UID:
edocfu_9959234698702883
Format:
1 online resource (388 p.)
ISBN:
1-281-91192-5
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9786611911928
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981-277-210-3
Series Statement:
K & E series on knots and everything ; v. 39
Content:
This is the first of three volumes collecting the original and now classic works in topology written in the 50s-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated "Singular homologies of fibre spaces."This is the translation of the Russian edition published in 2005 with one entry (Milnor's lectures on the h-cobordism) omitted.
Note:
Description based upon print version of record.
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Contents; 2. Definition. Manifolds associated with a given finite polyhedron K; S. P. Novikov's Preface; 1 L. S. Pontrjagin. Smooth manifolds and their applications in homotopy theory (Translated by V. O. Manturov); Introduction; Chapter I. Smooth manifolds and their maps; 1. Smooth manifolds; The notion of smooth manifold; Smooth mappings; Certain ways of constructing smooth manifolds; 2. Embedding of a manifold into Euclidean space; Smooth mapping of a manifold to a manifold of larger dimension; The projection operation in the Euclidean space; The embedding theorem
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3. Nonproper points of smooth mapsGeneral position argument; The Dubovitsky Theorem; 4. Non-degenerate singular points of smooth mappings; Typical self-intersection points of mappings Mk ! E2k; Typical critical points of a real-valued function on a manifold; Typical singularities of mappings Mk ! E2k-1; Canonical form of typical critical points and typical singular points; Chapter II. Framed manifolds; 1. Smooth approximations of continuous mappings and deformations; The structure of neighbourhood of a smooth manifold; Smooth approximations; 2. The basic method
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From framed manifolds to mappings 3. Homology group of framed manifolds; Homotopy of framed manifolds; The homology group k of framed manifolds; Orthogonalization of framings; 4. The suspension operation; Chapter III. The Hopf invariant; 1. Homotopy classification of mappings of n-manifolds to the n-sphere; Mapping degree; Mappings from Sn to Sn; Mappings from n-dimensional manifold to the n-sphere; 2. The Hopf invariant of mappings 2k+1 Sk+1; The linking coefficient; The Hopf invariant; The Hopf invariant of a framed manifold; 3. Framed manifolds with Hopf invariant equal to zero
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The surgeryManifolds with zero Hopf invariant; Chapter IV. Classification of mappings Sn+2 . Sn; 1. The Euclidean space rotation group; Quaternions; Covering homotopy; Torsion group of Euclidean space; 2. Classification of mappings 3 S2; Sphere-to-circle mappings; Hopf mapping of the 3-sphere to the 2-sphere; Classification of mappings S3 ! S2; 3. Classification of mappings from (n + 1)-sphere to n-sphere; Improving the framed manifold that performs the homology; Invariant ツ of mappings ーn+1 ィ Sn; The classification of mappings n+1 ! Sn; 4. Classification of mappings (n+2) Sn
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References2 R. Thom. Some "global" properties of di erentiable manifolds (Translated by V. O. Manturov with M. M. Postnikov's comments (1958)); Introduction; Chapter I. Properties of di.erentiable mappings; 1. Definitions; 2. Pre-image of a regular value; 3. Properties of the critical values set f( ); 3a. Pre-image of a manifold.; 4. Pre-image of a manifold under a t-regular mapping; 5. The isotopy theorem; Chapter II. Submanifolds and homology classes of a manifold; 1. Formulation of the problem; 2. The space adjoint to a subgroup of the orthogonal group
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3. The main theorem
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English
Additional Edition:
ISBN 981-270-559-7
Language:
English
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