By William S. Massey

ISBN-10: 0387902716

ISBN-13: 9780387902715

Ocr'd

William S. Massey Professor Massey, born in Illinois in 1920, bought his bachelor's measure from the college of Chicago after which served for 4 years within the U.S. military in the course of global struggle II. After the battle he bought his Ph.D. from Princeton college and spent extra years there as a post-doctoral study assistant. He then taught for ten years at the college of Brown college, and moved to his current place at Yale in 1960. he's the writer of various learn articles on algebraic topology and similar issues. This ebook built from lecture notes of classes taught to Yale undergraduate and graduate scholars over a interval of numerous years.

**Read Online or Download Algebraic Topology: An Introduction PDF**

**Similar topology books**

**New PDF release: Geometry Revisited**

This can be a arithmetic ebook, no longer a programming ebook, even though it explains Pascal to newcomers. it truly is geared toward highschool scholars and undergraduates with a robust curiosity in arithmetic, and lecturers searching for clean principles. it really is packed with diversified mathematical rules requiring little historical past. It encompasses a huge variety of not easy difficulties, lots of which illustrate how numerical computation ends up in conjectures which may then be proved by means of mathematical reasoning.

**Absolute Measurable Spaces (Encyclopedia of Mathematics and by Togo Nishiura PDF**

Absolute measurable area and absolute null area are very outdated topological notions, constructed from famous evidence of descriptive set thought, topology, Borel degree thought and research. This monograph systematically develops and returns to the topological and geometrical origins of those notions. Motivating the improvement of the exposition are the motion of the crowd of homeomorphisms of an area on Borel measures, the Oxtoby-Ulam theorem on Lebesgue-like measures at the unit dice, and the extensions of this theorem to many different topological areas.

**New PDF release: Ordering Braids (Mathematical Surveys and Monographs)**

Within the fifteen years because the discovery that Artin's braid teams get pleasure from a left-invariant linear ordering, a number of rather diversified techniques were used to appreciate this phenomenon. This publication is an account of these techniques, which contain such diverse gadgets and domain names as combinatorial workforce conception, self-distributive algebra, finite combinatorics, automata, low-dimensional topology, mapping classification teams, and hyperbolic geometry.

**New PDF release: Topologie Générale: Chapitres 5 à 10**

Topologie générale, Chapitres five � 10Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce deuxième quantity du Livre de Topologie générale, troisième Livre du traité, décrit de nombreux outils fondamentaux en topologie et en examine, tels que le théorème d’Urysohn, le théorème de Baire ou les espaces polonais.

- Combinatorial Methods in Topology and Algebra
- Gems, Computers and Attractors for 3-Manifolds (Series on Knots and Everything)
- Topology (Pure & Applied Mathematics)
- Algebraic topology
- Geometric asymptotics

**Additional info for Algebraic Topology: An Introduction**

**Example text**

C) We shall use the Euler characteristic to distinguish between compact surfaces. We shall achieve this purpose with complete rigor in a later chapter by the use of the fundamental group. 1 Let SI and 82 be compact surfaces. The Euler characteristics of SI and 82 and their connected sum, SI # 82, are related by the formula X031 #32) = X031) + X032) — 2PROOF: The proof is very simple; assume SI and 82 are triangulated. Form their connected sum by removing from each the interior of a triangle, and then identifying edges and vertices of the boundaries of the removed triangles.

Ary of a disc. 14 2 2 A triangulation of a torus. 3 1 18 / CHAPTER ONE Two-Dimensional Manifolds with the Opposite sides identiﬁed. There are 9 vertices, and the following 18 triangles: 124 245 235 356 361 146 457 578 658 689 649 479 187 128 289 239 379 137 We conclude our discussion of triangulations by noting that any triangulation of a compact surface satisﬁes the following two conditions: (1) Each edge is an edge of exactly two triangles. (2) Let 2) be a vertex of a triangulation. Then we may arrange the set of all triangles with v as a vertex in cyclic order, T0, T1, T2, .

It is clear that we can also work the process described above backwards; whenever there are three pairs of the second kind, we can replace them by one pair of the second kind and two pairs of the ﬁrst kind. 1 to any connected sum of which three or more of the summands are projective planes. 1, which may be preferable in some cases, results. 2 Any compact, orientable surface is homeomorphic to a sphere or a connected sum of tori. Any compact, nonorientable surface is homeomorphic to the connected sum of either a projective plane or Klein Bottle and a compact, orientable surface.

### Algebraic Topology: An Introduction by William S. Massey

by Jeff

4.3