A First Course in Algebraic Topology by Czes Kosniowski PDF

By Czes Kosniowski

ISBN-10: 0521298644

ISBN-13: 9780521298643

This self-contained advent to algebraic topology is appropriate for a few topology classes. It includes approximately one zone 'general topology' (without its traditional pathologies) and 3 quarters 'algebraic topology' (centred round the primary staff, a with ease grasped subject which provides a good suggestion of what algebraic topology is). The ebook has emerged from classes given on the collage of Newcastle-upon-Tyne to senior undergraduates and starting postgraduates. it's been written at a degree in order to allow the reader to take advantage of it for self-study in addition to a direction e-book. The strategy is leisurely and a geometrical flavour is obvious all through. the various illustrations and over 350 routines will end up worthy as a educating relief. This account may be welcomed by means of complicated scholars of natural arithmetic at schools and universities.

Show description

Read or Download A First Course in Algebraic Topology PDF

Best topology books

Get An Invitation to Morse Theory (2nd Edition) (Universitext) PDF

This self-contained remedy of Morse concept makes a speciality of functions and is meant for a graduate path on differential or algebraic topology. The e-book is split into 3 conceptually targeted elements. the 1st half comprises the rules of Morse conception. the second one half includes purposes of Morse concept over the reals, whereas the final half describes the fundamentals and a few functions of advanced Morse thought, a.

Read e-book online A book of curves PDF

This booklet opens up an immense box of arithmetic at an common point, one during which the component of aesthetic excitement, either within the shapes of the curves and of their mathematical relationships, is dominant. This publication describes equipment of drawing aircraft curves, starting with conic sections (parabola, ellipse and hyperbola), and occurring to cycloidal curves, spirals, glissettes, pedal curves, strophoids and so forth.

Prof. Dr. Klaus Jänich (auth.)'s Topologie PDF

Jetzt in der achten Auflage, behandelt dieses bewährte Lehrbuch die Aspekte der mengentheoretischen Topologie, die jeder Mathematikstudent in mittleren Semestern kennen sollte. "Das erklärte Ziel des Autors conflict es, von der mengentheoretischen Topologie in leicht faßlicher und anregender shape 'gerade so viel zu bringen, wie ein Mathematikstudent beherrschen sollte.

Download e-book for kindle: The Hodge Theory of Projective Manifolds by Mark Andrea A De Cataldo

This booklet is a written-up and extended model of 8 lectures at the Hodge concept of projective manifolds. It assumes little or no historical past and goals at describing how the speculation turns into steadily richer and extra appealing as one specializes from Riemannian, to Kähler, to complicated projective manifolds.

Additional resources for A First Course in Algebraic Topology

Example text

10 Definition Suppose that X is a topological space and G is a group then we say that X is a G-space if G acts on X and if the function 0g given by x -+ g E G. 11 Exercise Suppose that x is a G-space. Prove that the function 0g given by x -, is a homeomorphism from X to itself for all g E G. Deduce that there is a homomorphism from G to the group of homeomorphisms of X. Because of the above exercise we sometimes say that if X is a G-space then G is a group of homeomorphlsms of X. Using this we prove the next result.

What if we cut along a line one-third of the distance between the edges? The next result gives sufficient conditions to ensure that quotients of homeomorphic spaces are homeomorphic. 5 Theorem Let f: X —* Y be a function between the topological spaces X and Y. Suppose that X and Y have equivalence relations respectively and such that x if and only if f(x) f(x'). If f is a homeomorphism then and are homeomorphic. Proof Define a function F: -+ by F [x] = [f(x)], where the square brackets denote equivalence classes.

5 explains the intuitive idea of a 'homeomorphism' as presented in Chapter 4: We start with a space W. By cutting it we get X and a relation which tells us how to reglue X in order to get W. Now perform a homeomorphism f on X to give Y with an equivalence relation NaturAs an example consider x ally, we want that x x' • f(x) y f(x'). 5 the space Regluing Y according to Z is homeomorphic to the space X. A concept that we shall find useful later on is that of a group G 'acting' on a set X. The notion is fruitful and leads to examples of spaces with the quotient topology.

Download PDF sample

A First Course in Algebraic Topology by Czes Kosniowski


by Robert
4.5

Rated 4.24 of 5 – based on 34 votes