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143
Polynomialtime homology for simplicial Eilenberg–MacLane spaces
, 2013
"... In an earlier paper of Čadek, Vokř́ınek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all possible homotopy classes of maps between two topological spaces, under suitable restriction on the spaces. We aim a ..."
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at showing that, if the dimensions of the considered spaces are bounded by a constant, then the computations can be done in polynomial time. In this paper we make a significant technical step towards this goal: we show that the Eilenberg–MacLane space K(Z, 1), represented as a simplicial group, can
New relationships among loopspaces, symmetric products, and Eilenberg MacLane spaces
 in Cohomological Methods in Homotopy Theory (Barcelona, 1998), Birkhauser Verlag Progress in Math
"... Abstract. Let T (j) be the dual of the jth stable summand of Ω2S3 (at the prime 2) with top class in dimension j. Then it is known that T (j) is a retract of a suspension spectrum, and that the homotopy colimit of a certain sequence T (j) ! T (2j) ! : : : is an innite wedge of stable summands of K(V ..."
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Cited by 4 (1 self)
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(V; 1)’s, where V denotes an elementary abelian 2 group. In particular, when one starts with T (1), one gets K(Z=2; 1) = RP1 as one of the summands. I discuss a generalization of this picture using higher iterated loopspaces and Eilenberg MacLane spaces. I consider certain nite spectra T (n; j) for n
REGS REPORT: THE MORAVA ETHEORY OF EILENBERGMAC LANE SPACES
"... Chromatic homotopy, the confluence of stable homotopy and the geometry of formal groups, uses the following dictionary to interpret some of its basic tools: Spectrum Name Geometric counterpart MU complex cobordism moduli stack of formal groups, ..."
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Chromatic homotopy, the confluence of stable homotopy and the geometry of formal groups, uses the following dictionary to interpret some of its basic tools: Spectrum Name Geometric counterpart MU complex cobordism moduli stack of formal groups,
Dieudonné modules and pdivisible groups associated with Morava Ktheory of EilenbergMac Lane spaces,” Algebr. Geom. Topol
, 2007
"... Abstract. We study the structure of the formal groups associated to the Morava Ktheories of integral EilenbergMac Lane spaces. The main result is that every formal group in the collection {K(n) ∗ K(Z, q), q = 2, 3,...} for a fixed n enters in it together with its Serre dual, an analogue of a prin ..."
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Cited by 2 (0 self)
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Abstract. We study the structure of the formal groups associated to the Morava Ktheories of integral EilenbergMac Lane spaces. The main result is that every formal group in the collection {K(n) ∗ K(Z, q), q = 2, 3,...} for a fixed n enters in it together with its Serre dual, an analogue of a
On the computability of the plocal homology of twisted cartesian products of EilenbergMac Lane spaces
, 1999
"... Working in the framework of the Simplicial Topology, a method for calculating the plocal homology of a twisted cartesian product X(#, m, #, # # , n) = K(#, m) # K(# # , n) of EilenbergMac Lane spaces is given. The chief technique is the construction of an explicit homotopy equivalence between the ..."
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Working in the framework of the Simplicial Topology, a method for calculating the plocal homology of a twisted cartesian product X(#, m, #, # # , n) = K(#, m) # K(# # , n) of EilenbergMac Lane spaces is given. The chief technique is the construction of an explicit homotopy equivalence between
4. Categories of kinvariants and EilenbergMacLane objects 9
"... Abstract. We give a functorial construction of kinvariants for ring spectra, and use these to classify extensions in the Postnikov tower of a ring spectrum. Contents ..."
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Abstract. We give a functorial construction of kinvariants for ring spectra, and use these to classify extensions in the Postnikov tower of a ring spectrum. Contents
Research Article On the size of the third homotopy group of the suspension of an Eilenberg{MacLane space
"... Abstract: The nonabelian tensor square G G of a group G of jGj = pn and jG′j = pm (p prime and n;m 1) satis es a classic bound of the form jG Gj pn(nm). This allows us to give an upper bound for the order of the third homotopy group 3(SK(G; 1)) of the suspension of an Eilenberg{MacLane space K(G; ..."
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Abstract: The nonabelian tensor square G G of a group G of jGj = pn and jG′j = pm (p prime and n;m 1) satis es a classic bound of the form jG Gj pn(nm). This allows us to give an upper bound for the order of the third homotopy group 3(SK(G; 1)) of the suspension of an Eilenberg{MacLane space K
New cohomological relationships among loopspaces, symmetric products, and Eilenberg MacLane spaces
, 1996
"... Abstract. Let T (j) be the dual of the jth BrownGitler spectrum (at the prime 2) with top class in dimension j. Then it is known that T (j) is a retract of a suspension spectrum, is dual to a stable summand of Ω2S3, and that the homotopy colimit of a certain sequence T (j) ! T (2j) ! : : : is a wed ..."
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Cited by 3 (3 self)
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Abstract. Let T (j) be the dual of the jth BrownGitler spectrum (at the prime 2) with top class in dimension j. Then it is known that T (j) is a retract of a suspension spectrum, is dual to a stable summand of Ω2S3, and that the homotopy colimit of a certain sequence T (j) ! T (2j) ! : : : is a wedge of stable summands of K(V; 1)’s, where V denotes an elementary abelian 2 group. In particular, when one starts with T (1), one gets K(Z=2; 1) = RP1 as one of the summands. Re ning a question posed by Doug Ravenel, I discuss a generalization of this picture. I consider certain nite spectra T (n; j) for n; j 0 (with T (1; j) = T (j)), dual to summands of Ωn+1SN, conjecture generalizations of all of the above, and prove that all these conjectures are correct in cohomology. So, for example, T (n; j) has unstable cohomology, and the cohomology of the colimit of a certain sequence T (n; j) ! T (n; 2j) ! : : : agrees with the cohomology of the wedge of stable summands of K(V; n)’s corresponding to the wedge occurring in the n = 1 case above.
STRICT MODULES AND HOMOTOPY MODULES IN STABLE HOMOTOPY
 HOMOLOGY, HOMOTOPY AND APPLICATIONS, VOL.7(1), 2005, PP.39–49
, 2005
"... Let R be any associative ring with unit and let HR denote the corresponding Eilenberg–Mac Lane spectrum. We show ..."
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Let R be any associative ring with unit and let HR denote the corresponding Eilenberg–Mac Lane spectrum. We show
Results 11  20
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143