The homology of iterated loop spaces

By Vladimir A. Smirnov. 2000

381 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9a1e18e8f9446ced9113fc820fcf5f0f3689399a

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Citations in the corpus

Algebraic models in geometry (2008, background): “The case n = 2 requires more care and is done in detail in [61].”
Combinatorial operad actions on cochains (2001, neutral): “The morphism Z(r)∗ →Z(r)∗−r+1 is due to Smirnov ([26, 27]).”
Operads and Cosimplicial Objects: An Introduction (2004, methodology): “About 10 years later, Fred Cohen showed that if X has a C2 action then H∗X is a Gerstenhaber algebra (but he didn’t use this terminology); see [7].”
Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields (2009, neutral): “(1) the configuration space Confn of n points in the plane [12], [4]; (2) the moduli space Mg of smooth projective curves of genus g [34] (more precisely, the moduli stack; its homology is taken to be orbifold homology); (3) classifying spaces of arithmetic groups, e.”
On loop spaces of configuration spaces (2002, methodology): “Some cases for which the homology is understood are given when M = N×R(1) for a manifold N [4, 9], while some beautiful general results in characteristic zero are given in [23, 29].”
The Geometry of Iterated Loop Spaces (2007, background): “The observations of §8, which simplify and generalize results originally proved by Milgram [23], Tsuchiya [32], and myself within the geometric framework developed by Dyer and Lashof [11], include all of the geometry required for the computation of the Pontryagin ring of the monoid F of based…”
Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory (2014, positive): “The point is that, in general, is group completion [ 9 , 10 , 30 ], and so we have the level-wise group completion [ 25 , 2.2]).”
Operads, algebras, modules and motives (2018, background): “Its group Z r (X; q) of q-simplices in Adams grading r is free Abelian on the set of those codimension r irreducible subvarieties of X q which meet all faces properly, where q = Spec(F t 0 ; : : : ; t q ]”
A bordism approach to string topology (2003, neutral): “H⁄(›2X); this is due to F. Cohen [ 10 ]. Both examples are related by the Deligne’s conjecture proved in many dierent ways by C. Berger and B. Fresse [6], M. Kontsevich [32], M. Kontsevich and Y. Soibelman [33], J. McClure and J. Smith [39], D. Tamarkin [43] and S. Voronov [45].”
Tate cohomology and periodic localization of polynomial functors (2003, methodology): “Standard homology calculations as in [ CLM ,BMMS] imply the next lemma.”
Structured Ring Spectra: Moduli spaces of commutative ring spectra (2004, methodology): “The operations β Q can be assembled into an algebra R over Fp using the Adem relations (see [11], §I.”
Higher-order representation stability and ordered configuration spaces of manifolds (2016, neutral): “The (counterclockwise) fundamental chain of S 1 induces a map Theorem 3.4 (Cohen [12, Chapter III]) Fix n (cid:21) 2 .”