m392c_EHT_notes.tex

\documentclass[openany]{style_EHT}
\input{macros}
\begin{document}

\includepdf[fitpaper=true]{ESHT_Pulp_Cover.pdf}

\frontmatter
\tableofcontents

\section{Introduction}
	\input{introduction}

\mainmatter

\chapter{Unstable equivariant homotopy theory}
\section{$G$-spaces}
	\input{1_17_overview}
\section{$G$-CW complexes and Whitehead's theorem}
	\input{1_19_homotopy_theory_of_g_spaces}
\section{Elmendorf's theorem}
	\input{1_24_orbit_category}
\section{Bredon cohomology}
	\input{1_26_bredon_cohomology}
\section{Smith theory and the localization theorem}
	\input{1_31_smith_theory}
\section{The Sullivan conjecture}
	\input{2_2_sullivan}
\section{Question-and-answer session: 2/2/17}
	\input{2_2_q_and_a}

\chapter{Building the equivariant stable category}
\section{Dualities: Alexander, Spanier-Whitehead, Atiyah, Poincaré}
	\input{2_7_stable_category}
\section{Transfers and the Burnside category}
	\input{2_9_burnside}
\section{Diagram spectra}
	\input{2_9_diagram_spectra}
\section{Homotopy theory of diagram spectra}
	\input{2_14_homotopy_theory_of_spectra}
\section{The equivariant stable category}
	\input{2_16_equivariant_stable_category}
\section{The Wirthmüller isomorphism}
	\input{2_21_wirthmuller}
\section{Tom Dieck splitting}
	\input{2_23_tom_dieck}
\section{Question-and-answer session II: 2/24/17}
	\input{2_24_q_and_a}

\chapter{Mackey functors and $\RO(G)$-graded cohomology}
\section{The Burnside category}
	\input{2_28_burnside}
\section{Mackey functors}
	\input{3_2_mackey_functors}
\section{Brown representability and $\RO(G)$-graded cohomology theories}
	\input{3_7_brown_representability}
\section{Eilenberg-Mac Lane spectra}
	\input{3_21_eilenberg_mac_lane}
\section{Calculation of $\protect\underline H_{C_2}^{p,q}(*; \protect\underline{\Z})$}
	\input{3_23_constant_computation}
\section{Calculation of $\protect\underline H_{C_2}^{p,q}(*; A_{C_2})$}
	\input{3_23_burnside_computation}

\chapter{Multiplicative structures in the equivariant stable category}
\section{Operadic multiplication and $N_\infty$ operads}
	\input{3_30_multiplicative_structure}
\section{Green functors}
	\input{4_11_more_multiplicative_structure}
\section{Tambara functors}
	\input{4_13_composition_and_bispans}
\section{The Evens norm}
	\input{4_18_evens_norm}
\section{Equivariant $\Gamma$-spaces}
	\input{4_20_equivariant_gamma_spaces}
\section{The HHR norm}
	\input{4_20_change_of_universe}
\section{Consequences of the construction of the norm map}
	\input{4_25_norm_consequences}

\chapter{Spectral sequences}
\section{Tate spectra}
	\input{4_27_tate_spectra}
\section{The slice spectral sequence}
	\input{5_2_slice}
\section{The homotopy fixed point spectral sequence}
	\input{5_15_homotopy_fixed_points}

\backmatter

\clearpage
\fancyhead[LO]{\small\itshape Bibliography}
\bibliography{references}{}
\bibliographystyle{alpha}

%\clearpage
%\fancyhead[LO]{\small\itshape Index}
%\printindex

\end{document}