By William S. Massey

Ocr'd

William S. Massey Professor Massey, born in Illinois in 1920, acquired his bachelor's measure from the college of Chicago after which served for 4 years within the U.S. army in the course of international conflict II. After the battle he obtained his Ph.D. from Princeton collage and spent extra years there as a post-doctoral study assistant. He then taught for ten years at the college of Brown collage, and moved to his current place at Yale in 1960. he's the writer of diverse examine articles on algebraic topology and comparable subject matters. This publication built from lecture notes of classes taught to Yale undergraduate and graduate scholars over a interval of numerous years.

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

**Similar topology books**

**Prospects in topology: proceedings of a conference in honor of William Browder**

This assortment brings jointly influential papers via mathematicians exploring the study frontiers of topology, essentially the most vital advancements of recent arithmetic. The papers hide a variety of topological specialties, together with instruments for the research of team activities on manifolds, calculations of algebraic K-theory, a end result on analytic buildings on Lie team activities, a presentation of the importance of Dirac operators in smoothing conception, a dialogue of the good topology of 4-manifolds, a solution to the well-known query approximately symmetries of easily attached manifolds, and a clean point of view at the topological class of linear differences.

**A geometric approach to homology theory**

The aim of those notes is to offer a geometric remedy of generalized homology and cohomology theories. The principal thought is that of a 'mock bundle', that's the geometric cocycle of a basic cobordism conception, and the most new result's that any homology conception is a generalized bordism conception.

**Introduction to Topology: Second Edition**

This quantity explains nontrivial purposes of metric area topology to research, truly constructing their courting. additionally, issues from hassle-free algebraic topology concentrate on concrete effects with minimum algebraic formalism. chapters think about metric area and point-set topology; the different 2 chapters discuss algebraic topological fabric.

This ebook develops rigorous foundations for parametrized homotopy concept, that's the algebraic topology of areas and spectra which are always parametrized via the issues of a base house. It additionally starts off the systematic research of parametrized homology and cohomology theories. The parametrized global offers the normal domestic for plenty of classical notions and effects, equivalent to orientation idea, the Thom isomorphism, Atiyah and Poincaré duality, move maps, the Adams and Wirthmüller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences.

- Geometric Topology: Joint U.S.-Israel Workshop on Geometric Topology June 10-16, 1992 Technion, Haifa, Israel
- Intuitive Topology (Mathematical World, Volume 4)
- New developments in the theory of knots
- Open Problems in Topology II
- Algebraic Topology Barcelona 1986: Proceedings of a Symposium held in Barcelona, April 2–8, 1986

**Extra resources for Algebraic Topology: An Introduction**

**Example text**

Because T’ is compact and S is a Hausdorff space, go is a closed map, and hence S has the quotient topology determined by go (see Section 1 of Appendix A). This is a rigorous mathematical statement of our intuitive idea that S is obtained by gluing the triangles T1, T2, . . together along the appropriate edges. The polygon we desire will be constructed as a quotient space of T’. Consider any of the edges 65, 2 g 2' _S_ 11.. - and one other triangle T,-, for which 1 g j < i. -) consists of an edge of the triangle T:- and an edge of the triangle T} We identify these two edges of the triangles T; and T;- by identifying points which map onto the same point of e,- (speaking intuitively, we glue together the triangles T:- and T;).

Pairs of the ﬁrst kind. 21). We shall show that we can transform the polygon so that the four sides in question are consecutive around the perimeter of the polygon. 20 A pair of edges of the ﬁrst kind. 21(b). Then, out along d and paste together along a to obtain (0), as desired. 21(c). 1. (c) 26 / CHAPTER ONE Two-Dimensional Manifolds second kind, this leads to the desired result because, in that case, the symbol must be of the form alblaI‘bflazbzaglbz‘l . . a;‘b;1 and the surface is the connected sum of n tori.

Bk denote the components of the boundary. , then T has exactly two edges which have one vertex in B,- but do not lie in 8;. Similarly, if e is an edge that has a vertex in B,- but does lie in B;, then e is an edge of two triangles, both of which meet 8;. It follows that the edges and triangles that meet B,- but do not lie in B,- can be arranged in one or more cycles of alternating edges and triangles, T1, 81, T2, 82, . , Tn, 8n, Tn+1 = T1, such that each e,- is an edge of T,- and Ti“, whereas each T,- has ej_1 and e,- as edges.