Spectra and the steenrod algebra
WebOn the hit problem for the Steenrod algebra in the generic degree and its applications. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Vol. 116, Issue. 2, ... Hai, Generators for the mod 2 cohomology of the Steinberg summand of Thom spectra over B( Z/2)n, J. Algebra 381 (2013), 164–175. WebFrom this structure, the Steenrod reduced power operations arise; this was axiomatized in [May70]. One perspective would regard this as the structure of an E 1algebra on the function spectrum (HF p)X, parametrizing maps from Xinto an Eilenberg-Mac Lane spectrum. Power operations and the Adem relations between them do not make use of the ...
Spectra and the steenrod algebra
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WebFinally, the Steenrod algebra Ais the quotient of the free (noncommutative) F 2-algebra on generators Sqi by the Adem relations. Remark 3.2. At odd primes, we write Pi for the ith … WebNorth-Holland Mathematical Library Spectra and the Steenrod Algebra: Modules over the Steenrod Algebra and the Stable Homotopy Category ScienceDirect.com by Elsevier.
WebSome of these arise in topology (the ordinary stable homotopy category of spectra, categories of equivariant spectra, and Bousfield localizations of these), and others in algebra (coming from the representation theory of groups or of Lie algebras, as well as the derived category of a commutative ring). WebThis ring is the Steenrod algebra. Remark 1.4. I’ve written this down as a colimit of cohomologies, but it might be better to think of it as the cohomology of some kind of limit of suspensions of Eilenberg-Mac Lane spaces along the maps above. This limit is what we’ll later call an ‘Eilenberg-Mac Lane spectrum’. 2
WebSome of these arise in topology (the ordinary stable homotopy category of spectra, categories of equivariant spectra, and Bousfield localizations of these), and others in algebra (coming from the representation theory of groups or of Lie algebras, as well as the derived category of a commutative ring). ... WebWe apply the tools of stable homotopy theory to the study of modules over the mod \(p\) Steenrod algebra \(A^{*}\). More precisely, let \(A\) be the dual of \(A^{*}\); then we study the category \(\mathsf{stable}(A)\) of unbounded cochain complexes of injective comodules over \(A\), in which the morphisms are cochain homotopy classes of maps ...
WebNov 6, 2024 · can con ne ourselves to the smaller Steenrod algebra when we study questions involving the use of cohomology operations for cohomology theories …
WebJan 1, 1983 · This chapter describes Z p - cohomology and the steenrod algebra. The foundation of this chapter is the identification of the Hopf algebras A p, and [H(Z p), H(Z … knee high flat heel bootsWeb1-ring spectra lifting a classical diagram of modules over the mod-2 Steenrod algebra. In an appendix we document how to organize Morava’s forms of K-theory into a sheaf of E 1-ring spectra. 1 Introduction Some of the main applications of modern algebraic topology, including the development of structured ring spectra [EKMM97, HSS00], have been to knee high frye bootsWebThe book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original ... knee high fringed boots