New Mathematical Monographs: Cubical Homotopy Theory 25 by Ismar Voli&263; download EPUB, PDF, DJV
9781107030251 1107030250 Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological spaces with an emphasis on cubical diagrams. The book contains more than 300 examples and provides detailed explanations of many fundamental results. Part I focuses on foundational material on homotopy theory, viewed through the lens of cubical diagrams: fibrations and cofibrations, homotopy pullbacks and pushouts, and the Blakers-Massey Theorem. Part II includes a brief example-driven introduction to categories, limits and colimits, an accessible account of homotopy limits and colimits of diagrams of spaces, and a treatment of cosimplicial spaces. The book finishes with applications to some exciting new topics that use cubical diagrams: an overview of two versions of calculus of functors and an account of recent developments in the study of the topology of spaces of knots.
9781107030251 1107030250 Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological spaces with an emphasis on cubical diagrams. The book contains more than 300 examples and provides detailed explanations of many fundamental results. Part I focuses on foundational material on homotopy theory, viewed through the lens of cubical diagrams: fibrations and cofibrations, homotopy pullbacks and pushouts, and the Blakers-Massey Theorem. Part II includes a brief example-driven introduction to categories, limits and colimits, an accessible account of homotopy limits and colimits of diagrams of spaces, and a treatment of cosimplicial spaces. The book finishes with applications to some exciting new topics that use cubical diagrams: an overview of two versions of calculus of functors and an account of recent developments in the study of the topology of spaces of knots.