Analysis Situs
Analysis Situs

Author: Oswald Veblen

Publisher:

Published: 1931

Total Pages: 218

ISBN-13:

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'Analysis situs' is the name used by Poincaré when he was creating, at the end of the 19th century, the area of mathematics known today as topology. These lectures contain what is probably the first text where Poincaré's results and ideas were summarized, and an attempt to systematically present this difficult new area of mathematics was made. Of the two streams of topology existing at that time, point set topology and combinatorial topology, it is the latter to which this book is almost totally devoted. The first four chapters present, in detail, the notion and properties (introduced by Poincaré) of the incidence matrix of a cell decomposition of a manifold. The author's main goal is to show how to reproduce main topological invariants of a manifold and their relations in terms of the incidence matrix.

The Concept of a Riemann Surface
The Concept of a Riemann Surface

Author: Hermann Weyl

Publisher: Courier Corporation

Published: 2013-12-31

Total Pages: 210

ISBN-13: 048613167X

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This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.

Two-Dimensional Homotopy and Combinatorial Group Theory
Two-Dimensional Homotopy and Combinatorial Group Theory

Author: Cynthia Hog-Angeloni

Publisher: Cambridge University Press

Published: 1993-12-09

Total Pages: 428

ISBN-13: 0521447003

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Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.