Introduction to algebraic topolgy by martin cardek

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Introduction to algebraic topolgy by martin cardek

https://khothuvien.cori!INTRODUCTION TO ALGEBRAIC TOPOLOGYMARTIN CADEKContents0.Foreword11.Basic notions and constructions22.CW-complexes53.Simplicial

Introduction to algebraic topolgy by martin cardek l and singular homology84.Homology of CW-complexes ami applications175.Singular cohomology24G.More homological algebra297.Products in cohomology3G8.Ve

ctor bundles ami Thom isomorphism429.Poincare duality4G10.Homotopy groups5511.Fundamental group6012.Homotopy ami CW-complexes6513.Homotopy excision an Introduction to algebraic topolgy by martin cardek

d HurewitztheoremG914.Short overview of some furthermethodsin homotopy theory7GReferences81Index820. ForewordThese notes form a brief overview of basi

Introduction to algebraic topolgy by martin cardek

c topics in a usual introductory course of algebraic topology. They have been prepared for my series of lectures at the Okayama University. They canno

https://khothuvien.cori!INTRODUCTION TO ALGEBRAIC TOPOLOGYMARTIN CADEKContents0.Foreword11.Basic notions and constructions22.CW-complexes53.Simplicial

Introduction to algebraic topolgy by martin cardek lity. However, in all such cases I have tried to give references to well known textbooks the list of which you can find at the end.I would like to exp

ress my acknowledgements to the Okayama University, and especially to Professor Mamoru Mimura for inviting me to Okayama. I am also gratefull to my Ph Introduction to algebraic topolgy by martin cardek

D. student Richard Lastovecki whose comments helped me to correct and improve the text.The notes are available online in electronic form athttp:// www

Introduction to algebraic topolgy by martin cardek

.math.muni.cz/" cadekDate: September 5. 2002.121. Basic notions and constructions1.1.Notation. The closure, the interior and the boundary of a topolog

https://khothuvien.cori!INTRODUCTION TO ALGEBRAIC TOPOLOGYMARTIN CADEKContents0.Foreword11.Basic notions and constructions22.CW-complexes53.Simplicial

Introduction to algebraic topolgy by martin cardek of n-tuplcs of real and complex numbers, respectively, with the standard norm ||.r|| =lx«|2- The setsDn = {*€Rn; ||x||< 1}.5n = {^€Rn+1; 11*11 = 1}ar

e the n-dimensional disc and the n-dimensional sphere, respectively.1.2.Categories of topological spaces. Every category consists of objects and morph Introduction to algebraic topolgy by martin cardek

isms between them. Morphisms f : A —* B ami g : B c can be composed into a morphism go f : .4 -— c and for every object B there is a morphism idfi : B

Introduction to algebraic topolgy by martin cardek

—* B such that id/jo/ = f and go idfi = g. The composition of morphisms is associative.The category with topological spaces as objects and continuous

https://khothuvien.cori!INTRODUCTION TO ALGEBRAIC TOPOLOGYMARTIN CADEKContents0.Foreword11.Basic notions and constructions22.CW-complexes53.Simplicial

Introduction to algebraic topolgy by martin cardek ntinuous maps f : (X, *) —* (Y, *) such that /(*) = * they form the category TOP,. Topological spaces X, .4 will be called a pair of topological space

s if .4 is a subspace of A’ (notation (X. .4)). The notation f : (X, 4) —» (y. B) means that f : X —* Y is a continuous map which preserves subspaces, Introduction to algebraic topolgy by martin cardek

i. e. /(.4) c B. The category TOP2 consists of pairs of topological spaces as objects and continuous maps f : (X, A) —> (Y. B) as morphisms. Finally.

Introduction to algebraic topolgy by martin cardek

'TOP2 will denote the category of pairs of topological spaces with base points in subspaces and continuous maps preserving both subspaces and base po

https://khothuvien.cori!INTRODUCTION TO ALGEBRAIC TOPOLOGYMARTIN CADEKContents0.Foreword11.Basic notions and constructions22.CW-complexes53.Simplicial