# On the homology of mapping spaces

Open Mathematics (2011)

- Volume: 9, Issue: 6, page 1232-1241
- ISSN: 2391-5455

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topSemën Podkorytov. "On the homology of mapping spaces." Open Mathematics 9.6 (2011): 1232-1241. <http://eudml.org/doc/269480>.

@article{SemënPodkorytov2011,

abstract = {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.},

author = {Semën Podkorytov},

journal = {Open Mathematics},

keywords = {Arone spectral sequence; Anderson spectral sequence; Vassiliev spectral sequence},

language = {eng},

number = {6},

pages = {1232-1241},

title = {On the homology of mapping spaces},

url = {http://eudml.org/doc/269480},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Semën Podkorytov

TI - On the homology of mapping spaces

JO - Open Mathematics

PY - 2011

VL - 9

IS - 6

SP - 1232

EP - 1241

AB - 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.

LA - eng

KW - Arone spectral sequence; Anderson spectral sequence; Vassiliev spectral sequence

UR - http://eudml.org/doc/269480

ER -

## References

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- [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 Zbl0255.55012
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- [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 Zbl0623.55009
- [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 Zbl0259.55004
- [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 Zbl0864.55017
- [12] Vassiliev V.A., Complements of Discriminants of Smooth Maps: Topology and Applications, Transl. Math. Monogr., 98, American Mathematical Society, Providence, 1992

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