An Illustrated Introduction to Topology and Homotopy
Auteur : Kalajdzievski Sasho
An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs.
The first part of the text covers basic topology, ranging from metric spaces and the axioms of topology through subspaces, product spaces, connectedness, compactness, and separation axioms to Urysohn?s lemma, Tietze?s theorems, and Stone-?ech compactification. Focusing on homotopy, the second part starts with the notions of ambient isotopy, homotopy, and the fundamental group. The book then covers basic combinatorial group theory, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The last three chapters discuss the theory of covering spaces, the Borsuk-Ulam theorem, and applications in group theory, including various subgroup theorems.
Requiring only some familiarity with group theory, the text includes a large number of figures as well as various examples that show how the theory can be applied. Each section starts with brief historical notes that trace the growth of the subject and ends with a set of exercises.
TOPOLOGY: Sets, Numbers, Cardinals, and Ordinals. Metric Spaces: Definition, Examples, and Basics. Topological Spaces: Definition and Examples. Subspaces, Quotient Spaces, Manifolds, and CW-Complexes. Products of Spaces. Connected Spaces and Path Connected Spaces. Compactness and Related Matters. Separation Properties. Urysohn, Tietze, and Stone-Čech. HOMOTOPY: Isotopy and Homotopy. The Fundamental Group of a Circle and Applications. Combinatorial Group Theory. Seifert-van Kampen Theorem and Applications. On Classifying Manifolds and Related Topics. Covering Spaces, Part 1. Covering Spaces, Part 2. Applications. Applications in Group Theory. Bibliography.
Date de parution : 03-2015
Ouvrage de 500 p.
17.1x24.1 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 123,78 €
Ajouter au panierDate de parution : 06-2012
Ouvrage de 500 p.
17.8x25.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 13 jours).
Prix indicatif 82,09 €
Ajouter au panierThèmes d’An Illustrated Introduction to Topology and Homotopy :
Mots-clés :
Cayley Graph; Tietze Transformations; visual approach to topology and homotopy theory; Homotopic Relative; applications in group theory; Brouwer Fixed Point Theorem; theory of covering spaces; Deformation Retract; metric spaces and the axioms of topology; Klein Bottle; subspaces; product spaces; connectedness; compactness; and separation axioms; Homotopy Class; Urysohn’s lemma; Tietze’s theorems; and Stone-Čech compactification; Open Subset; ambient isotopy; Metric Space; basic combinatorial group theory; Homotopically Equivalent; Seifert-van Kampen theorem; knots; and low-dimensional manifolds; Closed Subset; Path Component; Covering Space; Tietze Extension Theorem; Quotient Space; Ambient Isotopic; Path Connected; Continuous Mapping; Infinite Cyclic Group; Normal Subgroup; Open Neighborhood; Cauchy Sequence; Trefoil Knot; Topological Spaces; Fixed Point Property