Books in Algebraic topology

Shape Theory

1st Edition
Volume 26
January 1, 1982
S. Mardešic + 1 more
English
eBook
9 7 8 0 0 8 0 9 6 0 1 4 2

North-Holland Mathematical Library, Volume 26: Shape Theory: The Inverse System Approach presents a systematic introduction to shape theory by providing background materials, motivation, and examples, including shape theory and invariants, pro-groups, shape fibrations, and metric compacta. The publication first ponders on the foundations of shape theory and shape invariants. Discussions focus on the stability and movability of spaces, homotopy and homology pro-groups, shape dimension, inverse limits and shape of compacta, topological shape, and absolute neighborhood retracts. The text then takes a look at a survey of selected topics, including basic topological constructions and shape, shape dimension of metric compacta, complement theorems of shape theory, shape fibrations, and cell-like maps. The text ponders on polyhedra and Borsuk's approach to shape. Topics include shape category of metric compacta and metric pairs, homotopy type of polyhedra, and topology of simplicial complexes. The publication is a valuable source of data for researchers interested in the inverse system approach.

Introduction to Homological Algebra, 85

1st Edition
June 28, 1979
Joseph J. Rotman
English
Hardback
9 7 8 0 1 2 5 9 9 2 5 0 3
eBook
9 7 8 0 0 8 0 8 7 4 0 1 2

An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author’s attempt to make it lovable. This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and Ⓧ; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences. This book will be of interest to practitioners in the field of pure and applied mathematics.

Projective Transformations

1st Edition
May 12, 2014
P. S. Modenov + 1 more
Henry Booker + 2 more
English
eBook
9 7 8 1 4 8 3 2 6 1 4 9 2

Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserv... transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

Algebraic and Classical Topology

1st Edition
May 9, 2014
I. M. James
English
eBook
9 7 8 1 4 8 3 1 8 4 7 7 7

Algebraic and Classical Topology contains all the published mathematical work of J. H. C. Whitehead, written between 1952 and 1960. This volume is composed of 21 chapters, which represent two groups of papers. The first group, written between 1952 and 1957, is principally concerned with fiber spaces and the Spanier-Whitehead S-theory. In the second group, written between 1957 and 1960, Whitehead returns to classical topology after a long interval, and participates in the renewed assault on the problems which fascinated him most. This book will prove useful to mathematicians.

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Books in Algebraic topology

Shape Theory

Introduction to Homological Algebra, 85

Projective Transformations

Algebraic and Classical Topology