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2011 | 9 | 6 | 1232-1241
Tytuł artykułu

On the homology of mapping spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
6
Strony
1232-1241
Opis fizyczny
Daty
wydano
2011-12-01
online
2011-09-23
Twórcy
Bibliografia
  • [1] Ahearn S.T., Kuhn N.J., Product and other fine structure in polynomial resolutions of mapping spaces, Algebr. Geom. Topol., 2002, 2, 591–647 http://dx.doi.org/10.2140/agt.2002.2.591
  • [2] Anderson D.W., A generalization of the Eilenberg-Moore spectral sequence, Bull. Amer. Math. Soc., 1972, 78(5), 784–786 http://dx.doi.org/10.1090/S0002-9904-1972-13034-9
  • [3] Arone G., A generalization of Snaith-type filtration, Trans. Amer. Math. Soc., 1999, 351(3), 1123–1150 http://dx.doi.org/10.1090/S0002-9947-99-02405-8
  • [4] Bendersky M., Gitler S., The cohomology of certain function spaces, Trans. Amer. Math. Soc., 1991, 326(1), 423–440 http://dx.doi.org/10.2307/2001871
  • [5] Boardman J.M., Conditionally convergent spectral sequences, In: Homotopy Invariant Algebraic Structures, Baltimore, 1998, Contemp. Math., 239, American Mathematical Society, Providence, 1999, 49–84
  • [6] Bousfield A.K., On the homology spectral sequence of a cosimplicial space, Amer. J. Math., 1987, 109(2), 361–394 http://dx.doi.org/10.2307/2374579
  • [7] Bousfield A.K., Kan D.M., Homotopy Limits, Completions and Localizations, Lecture Notes in Math., 304, Springer, Berlin-New York, 1972 http://dx.doi.org/10.1007/978-3-540-38117-4
  • [8] McCarthy R., On n-excisive functors of module categories, preprint available at www.math.uiuc.edu/~randy/Vita/Papers/DEGCLT3.pdf
  • [9] Pirashvili T., Dold-Kan type theorem for Γ-groups, Math. Ann., 2000, 318(2), 277–298 http://dx.doi.org/10.1007/s002080000120
  • [10] Podkorytov S.S., Commutative algebras and representations of the category of finite sets, preprint available at http://arxiv.org/abs/1011.6192
  • [11] Shipley B.E., Convergence of the homology spectral sequence of a cosimplicial space, Amer. J. Math., 1996, 118(1), 179–207 http://dx.doi.org/10.1353/ajm.1996.0004
  • [12] Vassiliev V.A., Complements of Discriminants of Smooth Maps: Topology and Applications, Transl. Math. Monogr., 98, American Mathematical Society, Providence, 1992
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0084-1
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