Buch, Englisch, 510 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1620 g
Reihe: Modern Birkhäuser Classics
Buch, Englisch, 510 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1620 g
Reihe: Modern Birkhäuser Classics
ISBN: 978-3-0346-0188-7
Verlag: Birkhäuser
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques.
Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature.
Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
Reviews:
- Analele Universitatii din Timisoara
- Zentralblatt MATH
- Mathematical Reviews
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
Simplicial sets.- Model Categories.- Classical results and constructions.- Bisimplicial sets.- Simplicial groups.- The homotopy theory of towers.- Reedy model categories.- Cosimplicial spaces: applications.- Simplicial functors and homotopy coherence.- Localization.
