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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Introduction to Algebraic Topology
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Introduction to Algebraic Topology
Holger Kammeyer (Broschiert, Englisch)
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Beschreibung
This textbook provides a succinct introduction to algebraic topology. It follows a modern categorical approach from the beginning and gives ample motivation throughout so that students will find this an ideal first encounter to the field. Topics are treated in a self-contained manner, making this a convenient resource for instructors searching for a comprehensive overview of the area. It begins… with an outline of category theory, establishing the concepts of functors, natural transformations, adjunction, limits, and colimits. As a first application, van Kampen's theorem is proven in the groupoid version. Following this, an excursion to cofibrations and homotopy pushouts yields an alternative formulation of the theorem that puts the computation of fundamental groups of attaching spaces on firm ground. Simplicial homology is then defined, motivating the Eilenberg-Steenrod axioms, and the simplicial approximation theorem is proven. After verifying the axiomsfor singular homology, various versions of the Mayer-Vietoris sequence are derived and it is shown that homotopy classes of self-maps of spheres are classified by degree.The final chapter discusses cellular homology of CW complexes, culminating in the uniqueness theorem for ordinary homology. Introduction to Algebraic Topology is suitable for a single-semester graduate course on algebraic topology. It can also be used for self-study, with numerous examples, exercises, and motivating remarks included. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
21.06.2022
Sprache
Englisch
EAN
9783030983123
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Compact Textbooks in Mathematics
Sonderedition
Nein
Autor
Holger Kammeyer
Seitenanzahl
182
Einbandart
Broschiert
Schlagwörter
uniqueness of ordinary homology, Algebraic topology, Category theory, Singular homology, Singular homology vs simplicial, Cellular homology, Fundamental groupoid, Fundamental groupoid category, Fundamental groupoid van Kampen, Homotopy pushouts, Homotopy category, Homotopy pushout category, Simplicial homology, Relative homology absolute, Absolute homology relative
Thema-Inhalt
PBPD - Algebraische Topologie
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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