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1.
Birgit Richter 《Journal of Pure and Applied Algebra》2002,171(1):59-66
We show how topological André-Quillen homology can be related to the usual algebraic André-Quillen homology. To this end we construct an Atiyah-Hirzebruch spectral sequence starting with the algebraic version and converging to the topological theory. This determines topological André-Quillen homology in classical cases of étale and smooth algebras. 相似文献
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Michael A. Mandell 《Advances in Mathematics》2003,177(2):227-279
We show that the André-Quillen cohomology of an E∞ simplicial algebra with arbitrary coefficients and the topological André-Quillen cohomology of an E∞ ring spectrum with Eilenberg-Mac Lane coefficients may be calculated as the André-Quillen cohomology of an associated E∞ differential graded algebra. 相似文献
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Teimuraz Pirashvili 《Proceedings of the American Mathematical Society》2003,131(6):1687-1694
We obtain André-Quillen homology for commutative algebras using relative homological algebra in the category of functors on finite pointed sets.
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We develop a simple theory of André-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent CW-complexes. This puts certain results of Sullivan in a more conceptual framework. 相似文献
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Andrew Baker Helen Gilmour Philipp Reinhard 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2008,78(1):27-50
Topological André-Quillen homology for commutative S-algebras was introduced by Basterra following work of Kriz, and has been intensively studied by several authors. In this
paper we discuss it as a homology theory on CW commutative S-algebras and apply it to obtain results on minimal atomic p-local S-algebras which generalise those of Baker and May for p-local spectra and simply connected spaces. We exhibit some new examples of minimal atomic commutative S-algebras.
A. Baker was partially supported by a YFF Norwegian Research Council grant while at the University of Oslo in 2007–8, a Carnegie
Trust for the Universities of Scotland grant, and Intas grants 03-51-3251 and 06-1000017-8609.
H. Gilmour was supported by an EPSRC studentship.
P. Reinhard was supported by an ORS grant.
We would like to thank M. Basterra, P. Kropholler, M. Mandell, P. May, B. Richter, J. Rognes and S. Sagave for numerous helpful
comments. We are also very grateful to the referee for encouraging us to rethink significantly issues of notation and structure,
thus improving the structure of the paper. 相似文献
6.
Ayelet Lindenstrauss 《Israel Journal of Mathematics》1996,93(1):317-332
We assume given a ringA with unit, and a subcomplex of the reduced bar complex ofA. We assume that this subcomplex is a deformation retract of the whole complex and thus has homology equal to the Hochschild
homology ofA, but it will typically be smaller and easier to calculate with. We use these to construct (accordingly small) deformation
retracts for the reduced bar complexes ofA[t] andA[t,t
−1]. WhenA is a Banach algebra, we also do this construction forC
∞(S1;A).
Partially supported by N.S.F. Grant No. DMS 92-03398. 相似文献
7.
Nicholas J. Kuhn 《Advances in Mathematics》2006,201(2):318-378
Let K(n) be the nth Morava K-theory at a prime p, and let T(n) be the telescope of a vn-self map of a finite complex of type n. In this paper we study the K(n)*-homology of Ω∞X, the 0th space of a spectrum X, and many related matters.We give a sampling of our results.Let PX be the free commutative S-algebra generated by X: it is weakly equivalent to the wedge of all the extended powers of X. We construct a natural map
sn(X):LT(n)P(X)→LT(n)Σ∞(Ω∞X)+ 相似文献
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Arrangements of hyperplanes and Lie algebra homology 总被引:6,自引:0,他引:6
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Micheline Vigué -Poirrier 《Transactions of the American Mathematical Society》2002,354(10):3869-3882
We prove two similar results by quite different methods. The first one deals with augmented artinian algebras over a field: we characterize the trivial algebra structure on the augmentation ideal in terms of the maximality of the dimensions of the Hochschild homology (or cyclic homology) groups. For the second result, let be a 1-connected finite CW-complex. We characterize the trivial algebra structure on the cohomology algebra of with coefficients in a fixed field in terms of the maximality of the Betti numbers of the free loop space.
13.
Reinhold Hübl 《manuscripta mathematica》1992,77(1):63-70
In this note we use a topological version of Hochschild homology and cyclic homology of a commutative algebra, introduced
by P. Seibt in [Se2], to show, that periodic homology can be used to calculate the relative algebraic de Rham cohomology of a morphism of affine
Q-schemes of finite type as defined in [Ha], chapt. III, §4. 相似文献
14.
We study certain algebraic properties of the small quantum homology algebra for the class of symplectic toric Fano manifolds.
In particular, we examine the semisimplicity of this algebra, and the more general property of containing a field as a direct
summand. Our main result provides an easily verifiable sufficient condition for these properties which is independent of the
symplectic form. Moreover, we answer two questions of Entov and Polterovich negatively by providing examples of toric Fano
manifolds with non-semisimple quantum homology, and others in which the Calabi quasi-morphism is not unique.
相似文献
15.
Cristodor Ionescu 《代数通讯》2013,41(12):4801-4805
In this note we will prove that the Hochschild homology algebra of a topological algebra and its universally complete differential algebra are isomorphic in the case of a formally smooth morphism 相似文献
16.
We compute the André–Quillen (or Harrison) cohomology of an affine toric variety. The best results are obtained either in the general case for the first three cohomology groups, or in the case of isolated singularities for all cohomology groups, respectively. 相似文献
17.
BACH 《Commentarii Mathematici Helvetici》1994,69(1):163-168
The following people participated in this research: Antonio Campillo, Jorge Alberto Guccione, Juan José Guccione, María Julia
Redondo, Andrea Solotar and Orlando E. Villamayor. 相似文献
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Joan Millès 《Advances in Mathematics》2011,(6):5120
We study the André–Quillen cohomology with coefficients of an algebra over an operad. Using resolutions of algebras coming from the Koszul duality theory, we make this cohomology theory explicit and we give a Lie theoretic interpretation. For which operads is the associated André–Quillen cohomology equal to an Ext-functor? We give several criteria, based on the cotangent complex, to characterize this property. We apply it to homotopy algebras, which gives a new homotopy stable property for algebras over cofibrant operads. 相似文献