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arXiv · 2007.02467

Topics in Topology and Homotopy Theory

Garth Warner
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Abstract

This book is an account of certain topics in general and algebraic topology. Instead of laying out a synopsis of each chapter, here is a sample of some of what is taken up: 1) Nilpotency and its role in homotopy theory. 2) Bousfield's theory of the localization of spaces and spectra. 3) Homotopy limits and colimits and their applications. 4) The James construction, symmetric products, and the Dold$-$Thom theorem. 5) Brown and Adams representability in the setting of triangulated categories 6) Operads and the May$-$Thomason theorem on the uniqueness of infinite loop space machines. 7) The plus construction and theorems A and B of Quillen. 8) Hopkins' global picture of stable homotopy theory. 9) Model categories, cofibration categories, and Waldhausen categories. 10) The Dugundji extension theorem and its consequences.

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Garth Warner. 2022-12-04. Topics in Topology and Homotopy Theory. https://arxiv.org/abs/2007.02467

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