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Segal, Graeme

The topology of spaces of rational functions. (English) Zbl 0427.55006

Acta Math. 143, 39-72 (1979).
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Cited in 26 Reviews
Cited in 110 Documents

MSC:

55P35 Loop spaces
55P10 Homotopy equivalences in algebraic topology
58D15 Manifolds of mappings
30F99 Riemann surfaces
14E05 Rational and birational maps

Keywords:

set of rational functions; space of all continuous maps from the Riemann sphere to itself, which take infinity to 1; homotopy equivalence; configuration space
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References:

[1] Arnol’d, V. I., On some topological invariants of algebraic functions.Trudy Moskov Mat. Obsc., 21 (1970) (A.M.S. Translation:Trans. Moscow Math. Soc., 30–52).
[2] Atiyah, M. F. &Jones, J. D. S., Topological aspects of Yang-Mills theory.Comm. Math. Phys., 61 (1978), 97–118. · Zbl 0387.55009 · doi:10.1007/BF01609489
[3] Brockett, R., Some geometric questions in the theory of linear systems. Transactions on automatic control.Inst. Electrical and Electronics Engineers, 21 (1976), 449–455. · Zbl 0332.93040
[4] Cohen, F. R. Lada, T. J. & May, J. P.,The homology of iterated loop spaces. Springer Lecture Notes in Mathematics, 533 (1976). · Zbl 0334.55009
[5] Dold, A., Decomposition theorems forS(n)-complexes.Ann. of Math., 75 (1962), 8–16. · Zbl 0125.01201 · doi:10.2307/1970415
[6] Dold, A. &Thom, R. Quasifaserungen und unendliche symmetrische Produkte.Ann. of Math., 67 (1958), 239–281. · Zbl 0091.37102 · doi:10.2307/1970005
[7] Eells, J. &Wood J. C., Restrictions on harmonic maps of surfaces.Topology, 15 (1976), 263–266. · Zbl 0328.58008 · doi:10.1016/0040-9383(76)90042-2
[8] Hilton, P. &Roitberg, J., On the Zeeman comparison theorem for the homology of quasi-nilpotent fibrations.Quarterly J. Math. 27 (1976), 433–444. · Zbl 0342.55010 · doi:10.1093/qmath/27.4.433
[9] James, I. M. &Segal, G. B., On equivariant homotopy type.Topology, 17 (1978), 267–272. · Zbl 0403.57007 · doi:10.1016/0040-9383(78)90030-7
[10] Mattuck, A., Picard bundlesIllinois J. Math., 5 (1961), 550–564.
[11] May, J. P.,The geometry of iterated loop spaces. Springer Lecture Notes in Mathematics, 271 (1972). · Zbl 0244.55009
[12] McDuff, D., Configuration spaces of positive and negative particles.Topology, 14 (1975), 91–107. · Zbl 0296.57001 · doi:10.1016/0040-9383(75)90038-5
[13] McDuff, D. &Segal, G. B., Homology fibrations and the ”group completion” theorem.Inventiones Math., 31 (1976), 279–284. · doi:10.1007/BF01403148
[14] Nakaoka, M., Cohomology of symmetric products.J. Inst. Polytech., Osaka City Univ., 7 (1956), 121–144. · Zbl 0072.40503
[15] Rosenlicht, M., Generalized Jacobian varieities.Ann. of Math., 59 (1954), 505–530. · Zbl 0058.37002 · doi:10.2307/1969715
[16] Segal, G. B., Configuration spaces and iterated loop spaces.Inventiones Math., 21 (1973), 213–221. · Zbl 0267.55020 · doi:10.1007/BF01390197
[17] –, Classifying spaces and spectral sequences.Publ. Math. I.H.E.S. Paris, 34 (1968), 105–112. · Zbl 0199.26404
[18] –, Classifying spaces related to foliations.Topology, 17 (1978), 367–382. · Zbl 0398.57018 · doi:10.1016/0040-9383(78)90004-6
[19] Serre, J. P.,Groupes algébriques et corps de classes. Hermann, Paris, 1959. · Zbl 0097.35604
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