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Cubical homotopy theory / Brian A. Munson, United States Naval Academy, Maryland, Ismar Volić, Wellesley College, Massachusetts.

By: Munson, Brian A, 1976- [author.].
Contributor(s): Volić, Ismar, 1973- [author.].
Material type: materialTypeLabelBookSeries: New mathematical monographs: 25.Publisher: Cambridge : Cambridge University Press, 2015.Description: 1 online resource (xv, 631 pages) : digital, PDF file(s).Content type: text Media type: computer Carrier type: online resourceISBN: 9781139343329 (ebook).Subject(s): Homotopy theory | Cube | Algebraic topologyDDC classification: 514/.24 Online resources: Click here to access online Summary: 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 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.
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Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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 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.

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