Abstract
The aim of this note is to show how previous combinatorial calculations in the computation of the cohomology of configuration spaces can be considerably simplified by more conceptual arguments involving some representation theory. Since I first lectured on these results some other accounts have been given ([CT93, Str93]), partly overlapping with this. Nevertheless. it seemed still worthwhile to publish a full account of these considerations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Arnold: The Cohomology Ring of the Colored Braid Groups, Edinburgh Math. Notes 5 (1969), 138–140
J. M. Boardman, R. Vogt: Homotopy-everything H-spaces, Bull. AMS 74 (1968), 1117–1122
F. R. Cohen, T. Lada, J. P. May: The homology of iterated loop spaces, Lecture Notes in Math. 533 (1976)
F. R. Cohen: Artin’s braid groups and classical homotopy theory, Contemp. Math. 44 (1985), 207–220
F. R. Cohen: Artirís braid groups, classical homotopy theory, and sundry other curiosities, Contemp. Math. 78 (1988), 167–206
F. R. Cohen, J. P. May, L. R. Taylor: Splitting of certain spaces CX, Proc. Camb. Phil. Soc. 84 (1978), 465–496
F. R. Cohen, L. Taylor: Computations of Gelfand-Fuks cohomology, the cohomology of function spaces and the cohomology of configuration spaces, Lecture Notes in Math. 657 (1978), 106–143
F. R. Cohen, L. Taylor: On the representation theory associated to the cohomology of configuration spaces, Contemp. Math. 146 (1993), 167–206
E. Fadell, L. Neuwirth: Configuration spaces, Math. Scand. 10 (1962), 119–126
D. B. Fuks: Cohomologies of the group cos mod 2, Functional Analysis Appl. 4 (1970), 143–151
G. I. Lehrer: On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes, J. Algebra 104 (1986), 410–424
G. I. Lehrer: On the Poincaré series associated with Coxeter group actions on complements of hyperplanes, J. Lond. Math. Soc. 36 (1987), 275–294
G. I. Lehrer: A survey of Hecke algebras and the Artin braid groups, Contemp. Math. 78 (1988), 365–383
J. P. May: The geometry of iterated loop spaces, Springer Lecture Notes 271 (1972)
J. Rognes: The rank filtration in algebraic K-theory, Topology 31 (1993), 813–845
G. Segal: Configuration spaces and iterated loop spaces, Invent. Math. 21 (1973), 213–221
N. P. Strickland: Geometry and topology of configuration spaces, Preprint MIT 1993
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Birkhäuser Verlag
About this paper
Cite this paper
Ossa, E. (1996). On the cohomology of configuration spaces. In: Broto, C., Casacuberta, C., Mislin, G. (eds) Algebraic Topology: New Trends in Localization and Periodicity. Progress in Mathematics, vol 136. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9018-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9018-2_26
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9869-0
Online ISBN: 978-3-0348-9018-2
eBook Packages: Springer Book Archive