| 书目名称 | Introduction to Algebraic Topology | | 编辑 | Holger Kammeyer | | 视频video | | | 概述 | Offers a modern and concise introduction to algebraic topology.Features a short chapter on category theory, ideal for a first encounter to the field.Provides motivation for graduate students studying | | 丛书名称 | Compact Textbooks in Mathematics | | 图书封面 |  | | 描述 | 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 | | 出版日期 | Textbook 2022 | | 关键词 | uniqueness of ordinary homology; Algebraic topology; Category theory; Singular homology; Singular homolo | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-98313-0 | | isbn_softcover | 978-3-030-98312-3 | | isbn_ebook | 978-3-030-98313-0Series ISSN 2296-4568 Series E-ISSN 2296-455X | | issn_series | 2296-4568 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 19:26:07
