Gamma homology, Lie representations and E ? multiplications

Robinson, Alan

doi:10.1007/s00222-002-0272-5

Cited by 43 publications

(73 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If this was all we really wanted, the result is essentially due to Baker [6] in its A ∞ form, or one could follow Robinson [36] for the E ∞ case. 12 But Hopkins and Miller did much more.…”

Section: Hopkins-miller Solves a Moduli Problemmentioning

confidence: 99%

See 1 more Smart Citation

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

Goerss¹

2004

Axiomatic, Enriched and Motivic Homotopy Theory

View full text Add to dashboard Cite

In the first part of this article, I will state a realization problem for diagrams of structured ring spectra, and in the second, I will discuss the moduli space which parametrizes the problem.While some of what I say is quite general, the ring spectra I have in mind will arise from the chromatic point of view, which uses the geometry of formal groups to organize stable homotopy theory. Thus, a subsidiary aim here is to reemphasize this connection between algebraic geometry and homotopy theory.

show abstract

Section: Hopkins-miller Solves a Moduli Problemmentioning

confidence: 99%

“…It is this case for which Robinson's original obstruction theory (see [35] and [6]) applied, at least in the A ∞ case. More recently ( [36]) Robinson has an E ∞ version based on Gamma cohomology [37]. For 2.)…”

Section: Problem 21 (Realization Problem Iibis)mentioning

confidence: 99%

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

Goerss¹

2004

Axiomatic, Enriched and Motivic Homotopy Theory

View full text Add to dashboard Cite

show abstract

“…Alan Robinson then identifies E .Q m nC1 Ë † m E^m/ as some tractable algebraic object and induces homomorphism up to E E . Furthermore he proves in [24,Proposition 5.4] that obstruction are always cocycles for a suitable coboundary map, which then gives the final identification with Gamma cohomology groups.…”

Section: Where the Obstructions Come Frommentioning

confidence: 99%

“…Alan Robinson introduced this filtration in [24] and we will describe it in Section 3. We will prove Theorem 1.1 in Section 6.2.…”

Section: Theorem 11mentioning

confidence: 99%

A lower bound for coherences on the Brown–Peterson spectrum

Richter

2006

Algebr. Geom. Topol.

View full text Add to dashboard Cite

We provide a lower bound for the coherence of the homotopy commutativity of the Brown-Peterson spectrum, BP , at a given prime p and prove that it is at least .2p2 C 2p 2/-homotopy commutative. We give a proof based on Dyer-Lashof operations that BP cannot be a Thom spectrum associated to n-fold loop maps to BSF for n D 4 at 2 and n D 2p C 4 at odd primes. Other examples where we obtain estimates for coherence are the Johnson-Wilson spectra, localized away from the maximal ideal and unlocalized. We close with a negative result on Morava-K -theory. 55P43; 13D03

show abstract

“…In [17], Robinson makes explicit a small complex, analogous to Harrison's complex, which computes usual -homology. In the case where the operad P is Koszul, we define an explicit complex to compute the -homology associated to P. Recall that an operad is Koszul if we have a quasi-isomorphism between .P ı KP ı P; @/ and P, where KP is the Koszul construction, defined by K.P/ .s/ WD H s .B .P/ .s/ ; @/.…”

mentioning

confidence: 99%

Γ–homology of algebras over an operad

Hoffbeck

2010

Algebr. Geom. Topol.

View full text Add to dashboard Cite

-homology of algebras over an operad ERIC HOFFBECKThe purpose of this paper is to study generalizations of Gamma-homology in the context of operads. Good homology theories are associated to operads under appropriate cofibrancy hypotheses, but this requirement is not satisfied by usual operads outside the characteristic zero context. In that case, the idea is to pick a cofibrant replacement Q of the given operad P. We can apply to P-algebras the homology theory associated to Q in order to define a suitable homology theory on the category of P-algebras. We make explicit a small complex to compute this homology when the operad P is binary and Koszul. In the case of the commutative operad P D Com, we retrieve the complex introduced by Robinson for the Gamma-homology of commutative algebras. 16E40; 18D50, 18G55, 18G60The classical homology theories of commutative algebras (Harrison homology in the differential graded setting over a field of characteristic 0, see Harrison [11], and André-Quillen homology in the simplicial setting over a ring of any characteristic, see Quillen [16] and André [1]) can be considered as homology theories associated to the commutative operad Com. There is another homology theory for commutative algebras, -homology (Gamma-homology in plain words, also called topological André-Quillen), which has been introduced by Robinson and Whitehouse in [18], and by Basterra in [3] (with a different point of view), to solve obstruction problems in homotopy theory. In the setting of [18], Gamma-homology is defined as the homology theory associated to an E 1 -operad (a cofibrant replacement of Com). This new homology can be defined in the context of differential graded or simplicial context or in the context of spectra, and gives the same result in each case (see Mandell [15]), in contrast with the usual André-Quillen homology.The purpose of this paper is to study generalizations of -homology in the context of operads.

show abstract

Gamma homology, Lie representations and E ? multiplications

Cited by 43 publications

References 10 publications

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

A lower bound for coherences on the Brown–Peterson spectrum

Γ–homology of algebras over an operad

Contact Info

Product

Resources

About