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020 a| 9781470472481q| paperback;

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100 1 a| May, J. Peter0| http://id.loc.gov/authorities/names/n500070531| http://id.loc.gov/rwo/agents/n50007053.;

245 10 a| Equivariant infinite loop space theoryh| [electronic resource] :b| the space level story /c| J. Peter May, Mona Merling, Angélica M. Osorno.;

260 a| Providence, RI :b| American Mathematical Society,c| 2025.;

300 a| v, 136 pages ;c| 26 cm.;

334 a| single unitb| mono0| http://id.loc.gov/vocabulary/issuance/mono;

353 a| bibliographyb| bibliography0| http://id.loc.gov/vocabulary/msupplcont/bibliography;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 305, number 1540 (sixth of 7 numbers);

504 a| Includes bibliographical references.;

506 a| Available only to authorized users.;

520 a| "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 on the 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.;

538 a| Mode of access: World Wide Web;

650 0 a| Infinite loop spaces0| http://id.loc.gov/authorities/subjects/sh91003668;

650 0 a| Topological algebras0| http://id.loc.gov/authorities/subjects/sh85136079;

650 7 a| Algebraic topology -- Homotopy theory -- Stable homotopy theory, spectra2| msc;

650 7 a| Algebraic topology -- Homotopy theory -- Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)2| msc;

650 7 a| Algebraic topology -- Homotopy theory -- Equivariant homotopy theory2| msc;

650 7 a| Category theory; homological algebra -- General theory of categories and functors -- Functor categories, comma categories2| msc;

650 7 a| Category theory; homological algebra -- Abelian categories -- Derived categories, triangulated categories2| msc;

650 7 a| Algebraic topology -- Homotopy theory -- Loop space machines, operads2| msc;

650 7 a| Algebraic topology -- Applied homological algebra and category theory -- Abstract and axiomatic homotopy theory2| msc;

655 0 a| Electronic books.;

700 1 a| Merling, Mona0| http://id.loc.gov/authorities/names/no20250456311| http://id.loc.gov/rwo/agents/no2025045631.;

700 1 a| Osorno, Angélica M.0| http://id.loc.gov/authorities/names/no20250456331| http://id.loc.gov/rwo/agents/no2025045633.;

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758 4| http://id.loc.gov/ontologies/bibframe/instanceOf1| http://id.loc.gov/resources/works/24263405;

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Equivariant infinite loop space theory the space level story / J. Peter May, Mona Merling, Angélica M. Osorno.

Author/creator	May, J. Peter
Other author	Merling, Mona
Other author	Osorno, Angélica M.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2025.
Description	v, 136 pages ; 26 cm.
Supplemental Content	Full text available from eBooks on EBSCOhost
Subjects	Infinite loop spaces Topological algebras

Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 305, number 1540 (sixth of 7 numbers)
Abstract	"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 on the 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.
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2025010632
ISBN	9781470472481 paperback
ISBN	pdf

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Equivariant infinite loop space theory the space level story / J. Peter May, Mona Merling, Angélica M. Osorno.

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