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Cellular Ek-algebras / S. Galatius, A. Kupers, O. Randal-Williams.
Math/Physics/Astronomy - New Book Shelf QA1 .A85 v.460
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Log in to request item- Format:
- Book
- Author/Creator:
- Galatius, Søren, 1976- author.
- Kupers, Alexander, 1988- author.
- Randal-Williams, Oscar, 1983- author.
- Series:
- Astérisque ; 460.
- Astérisque, 0303-1179 ; 460
- Language:
- English
- French
- Subjects (All):
- Differential topology.
- Cobordism theory.
- Homology theory.
- CW complexes.
- Indecomposable modules.
- Homotopy theory.
- Loop spaces.
- Algebraic topology.
- Physical Description:
- x, 299 pages : illustrations ; 24 cm.
- Place of Publication:
- Paris : Société mathématique de France, 2025.
- Language Note:
- In English. Abstract also in French.
- Summary:
- We give a set of foundations for cellular Ek-algebras which are especially convenient for applications to homological stability. We provide conceptual and computational tools in this setting, such as filtrations, a homology theory for Ek-algebras with a Hurewicz theorem, CW approximations, and many spectral sequences, which shall be used for such applications in future papers. back cover
- Nous bâtissons les fondations de la théorie des Ek-algèbres cellulaires, en vue d'applications en stabilité homologique. Nous donnons des outils conceptuels et des outils de calcul, y compris des filtrations, une théorie d'homologie pour les Ek-algèbres avec un théorème de Hurewicz, des approximations cellulaires, et plusieurs suites spectrales. back cover
- Contents:
- Part I. Category theory of algebras over a monad
- Contexts for category theory
- Sifted monads and indecomposables
- Monads associated to operads
- Filtered algebras
- Cell attachments
- Part II. Homotopy theory of algebras over a monad
- Contexts for homotopy theory
- Homotopy theory of monads and indecomposables
- Homotopy theory of operads, algebras, and modules
- Homology and spectral sequences
- Hurewicz theorems and CW approximation
- Part III. Ek-algebras
- Ek-algebras and E1-modules
- Indecomposables and the bar construction
- Transferring vanishing lines
- Comparing algebra and module cells
- Wk-1-algebras
- Part IV. A framework for examples
- Ek-algebras from monoidal groupoids
- Application to homological stability
- Local coefficients
- Koszulity and connectivity.
- Notes:
- Includes bibliographical references (pages [285]-292) and index.
- ISBN:
- 9782379052194
- 2379052190
- OCLC:
- 1558599337
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