Some weak equivalences for classifying spaces
HTML articles powered by AMS MathViewer
- by Solomon M. Jekel PDF
- Proc. Amer. Math. Soc. 90 (1984), 469-476 Request permission
Abstract:
For topological categories $\mathcal {C}$ with fractions we give a model for the loops on the classifying space $\Omega B\mathcal {C}$ as a simplicial group which generalizes the fact that $\Omega B\mathcal {C} = \mathcal {C}$ when $\mathcal {C}$ is a topological group. This construction is applied to give some well-known, and some new, examples of weak equivalences between classifying spaces arising in the theory of foliations.References
-
P. Greenberg, A model for groupoids of homomorphisms, Thesis, M. I. T., 1982.
- Solomon M. Jekel, Loops on the classifying space for foliations, Amer. J. Math. 102 (1980), no. 1, 13–23. MR 556886, DOI 10.2307/2374170
- Solomon M. Jekel, Simplicial decomposition of $\Gamma$-structures, Bol. Soc. Mat. Mexicana (2) 26 (1981), no. 1, 13–20. MR 742011
- Solomon M. Jekel, Simplicial $K(G,1)$’s, Manuscripta Math. 21 (1977), no. 2, 189–203. MR 442923, DOI 10.1007/BF01168019
- W. G. Dwyer and D. M. Kan, Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980), no. 1, 17–35. MR 578563, DOI 10.1016/0022-4049(80)90113-9
- D. G. Quillen, Spectral sequences of a double semi-simplicial group, Topology 5 (1966), 155–157. MR 195097, DOI 10.1016/0040-9383(66)90016-4
- Graeme Segal, Categories and cohomology theories, Topology 13 (1974), 293–312. MR 353298, DOI 10.1016/0040-9383(74)90022-6
- Graeme Segal, Classifying spaces related to foliations, Topology 17 (1978), no. 4, 367–382. MR 516216, DOI 10.1016/0040-9383(78)90004-6
- John R. Stallings, The cohomology of pregroups, Conference on Group Theory (Univ. Wisconsin-Parkside, Kenosha, Wis., 1972), Lecture Notes in Math., Vol. 319, Springer, Berlin, 1973, pp. 169–182. MR 0382481
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 469-476
- MSC: Primary 57R32; Secondary 55P10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0728371-8
- MathSciNet review: 728371