By William Fulton

To the trainer. This publication is designed to introduce a pupil to a couple of the real rules of algebraic topology via emphasizing the re­ lations of those rules with different components of arithmetic. instead of settling on one viewpoint of modem topology (homotopy idea, simplicial complexes, singular concept, axiomatic homology, fluctuate­ ential topology, etc.), we focus our consciousness on concrete prob­ lems in low dimensions, introducing simply as a lot algebraic machin­ ery as worthwhile for the issues we meet. This makes it attainable to work out a greater diversity of vital positive aspects of the topic than is common in a starting textual content. The publication is designed for college kids of arithmetic or technological know-how who're no longer aiming to develop into working towards algebraic topol­ ogists-without, we are hoping, discouraging budding topologists. We additionally suppose that this process is in larger concord with the historic devel­ opment of the topic. What could we adore a pupil to grasp after a primary path in to­ pology (assuming we reject the reply: 1/2 what one would prefer the coed to grasp after a moment path in topology)? Our solutions to this have guided the alternative of fabric, including: below­ status the relation among homology and integration, first on aircraft domain names, afterward Riemann surfaces and in greater dimensions; wind­ ing numbers and levels of mappings, fixed-point theorems; appli­ cations equivalent to the Jordan curve theorem, invariance of area; in­ dices of vector fields and Euler features; primary groups

Show description

Read or Download Algebraic Topology: A First Course (Graduate Texts in Mathematics) PDF

Similar geometry & topology books

Download e-book for iPad: Metric and Differential Geometry: The Jeff Cheeger by Xianzhe Dai,Xiaochun Rong

Metric and Differential Geometry grew out of a equally named convention held at Chern Institute of arithmetic, Tianjin and Capital common college, Beijing. a few of the contributions to this quantity conceal a vast variety of subject matters in metric and differential geometry, together with metric areas, Ricci circulation, Einstein manifolds, Kähler geometry, index thought, hypoelliptic Laplacian and analytic torsion.

Download e-book for kindle: Differential Characters (Lecture Notes in Mathematics) by Christian Bär,Christian Becker

Delivering a scientific advent to differential characters as brought via Cheeger and Simons, this article describes very important strategies similar to fiber integration, better dimensional holonomy, transgression, and the product constitution in a geometrical demeanour. Differential characters shape a version of what's these days referred to as differential cohomology, that's the mathematical constitution at the back of the better gauge theories in physics.

New PDF release: Abstract Regular Polytopes (Encyclopedia of Mathematics and

Summary usual polytopes stand on the finish of greater than millennia of geometrical learn, which all started with usual polygons and polyhedra. they're hugely symmetric combinatorial constructions with unique geometric, algebraic or topological houses; in lots of methods extra attention-grabbing than conventional normal polytopes and tessellations.

Download PDF by J. A. Hillman: The Algebraic Characterization of Geometric 4-Manifolds

This booklet describes paintings, mostly that of the writer, at the characterization of closed 4-manifolds when it comes to ordinary invariants reminiscent of Euler attribute, basic workforce, and Stiefel–Whitney sessions. utilizing strategies from homological staff conception, the speculation of 3-manifolds and topological surgical procedure, infrasolvmanifolds are characterised as much as homeomorphism, and floor bundles are characterised as much as basic homotopy equivalence.

Extra info for Algebraic Topology: A First Course (Graduate Texts in Mathematics)

Example text

Download PDF sample

Algebraic Topology: A First Course (Graduate Texts in Mathematics) by William Fulton


by John
4.2

Rated 4.96 of 5 – based on 8 votes