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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