On the homology of mapping spaces

• Autorzy: Semën Podkorytov
• 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.

Słowa kluczowe

EN

Arone spectral sequence; Anderson spectral sequence; Vassiliev spectral sequence

Kategorie tematyczne

• 55T20: Eilenberg-Moore spectral sequences

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 6
• Strony: 1232-1241

Daty

wydano

2011-12-01

online

2011-09-23

Twórcy

autor

Semën Podkorytov

• Steklov Mathematical Institute at St. Petersburg

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

Identyfikatory

DOI

10.2478/s11533-011-0084-1