Atnaujinkite slapukų nuostatas

El. knyga: Introduction to Algebraic Topology

  • Formatas: EPUB+DRM
  • Serija: Compact Textbooks in Mathematics
  • Išleidimo metai: 20-Jun-2022
  • Leidėjas: Springer Nature Switzerland AG
  • Kalba: eng
  • ISBN-13: 9783030983130
Kitos knygos pagal šią temą:
Introduction to Algebraic TopologyDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Serija: Compact Textbooks in Mathematics
  • Išleidimo metai: 20-Jun-2022
  • Leidėjas: Springer Nature Switzerland AG
  • Kalba: eng
  • ISBN-13: 9783030983130
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

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 axioms for 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.

Recenzijos

Throughout the book there are many diagrams, pictures and nice examples to explain the concepts. The reviewer finds reading the book a pleasure. The reviewer recommends the book to any student taking a first course in algebraic topology . (Man-Ho Ho, Mathematical Reviews, April, 2023)



The book is beautifully laid out, with clearly marked offset examples and remarks, and some biographical information about some of the mathematicians referenced. The number of exercises is modest, with a few at the end of each chapter, but they seem to be thoughtfully designed to introduce new key concepts. This book should be a valuable resource for anyone teaching a course at this level. (Julie Bergner, zbMATH 1502.55001, 2023)

Basic notions of category theory.- Fundamental groupoid and van Kampen's theorem.- Homology: ideas and axioms.- Singular homology.- Homology: computations and applications.- Cellular homology.- Appendix: Quotient topology.

Holger Kammeyer is Assistant Professor of Algebra and Geometry at the University of Düsseldorf. His research interests include algebraic topology as well as arithmetic and profinite groups. A particular field of his expertise is the theory of ²-invariants on which he has authored the textbook Introduction to ²-invariants (Lecture Notes in Mathematics, Volume 2247, Springer).
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97830309831306e.html