Equivariant Infinite Loop Space Theory

J. Peter May, Mona Merling, Angelica M. Osorno

ISBN 10: 1470472481 / ISBN 13: 9781470472481

Published by American Mathematical Society, US, 2025

About this Item

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.

Seller Inventory # LU-9781470472481

Bibliographic Details

• Title: Equivariant Infinite Loop Space Theory
• Publisher: American Mathematical Society, US
• Publication Date: 2025
• Language: English
• ISBN 10: 1470472481
• ISBN 13: 9781470472481
• Binding: Paperback
• Condition: New

About this title

Synopsis

"We rework and generalize equivariant infinite loop space theory, which shows how to construct G-spectra from G-spaces with suitable structure. There is a classical version which gives classical -G-spectra for any topological group G, but our focus is onthe construction of genuine -G-spectra when G is finite. We also show what is and is not true when G is a compact Lie group. We give new information about the Segal and operadic equivariant infinite loop space machines, supplying many details that are missing from the literature, and we prove by direct comparison that the two machines give equivalent output when fed equivalent input. The proof of the corresponding nonequivariant uniqueness theorem, due to May and Thomason, works for classical G-spectra for general G but fails for genuine G-spectra. Even in the nonequivariant case, our comparison theorem is considerably more precise, giving an illuminating direct point-set level comparison. We have taken the opportunity to update this general area, equivariant and nonequivariant, giving many new proofs, filling in some gaps, and giving a number of corrections to results and proofs in the literature"-- Provided by publisher.