Volume 13 (2008)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Other MSP Publications

Symmetric products, duality and homological dimension of configuration spaces

Sadok Kallel

Geometry & Topology Monographs 13 (2008) 499–527

DOI: 10.2140/gtm.2008.13.499

Bibliography
1 M Aouina, J R Klein, On C T C Wall's suspension theorem, Forum Math. 18 (2006) 829–837 MR2265902
2 G Z Arone, W G Dwyer, Partition complexes, Tits buildings and symmetric products, Proc. London Math. Soc. (3) 82 (2001) 229–256 MR1794263
3 M F Atiyah, J D S Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978) 97–118 MR503187
4 P Bellingeri, S Gervais, J Guaschi, Lower central series for surface braid groups, preprint, Universita di Pisa (2006)
5 C F Bödigheimer, Stable splittings of mapping spaces, from: "Algebraic topology (Seattle, Wash. 1985)", Lecture Notes in Math. 1286, Springer (1987) 174–187 MR922926
6 C F Bödigheimer, F R Cohen, R J Milgram, Truncated symmetric products and configuration spaces, Math. Z. 214 (1993) 179–216 MR1240884
7 C F Bödigheimer, F Cohen, L Taylor, On the homology of configuration spaces, Topology 28 (1989) 111–123 MR991102
8 F R Cohen, The unstable decomposition of Ω 2Σ 2X and its applications, Math. Z. 182 (1983) 553–568 MR701370
9 F R Cohen, On the mapping class groups for punctured spheres, the hyperelliptic mapping class groups, SO(3), and Spinc(3), Amer. J. Math. 115 (1993) 389–434 MR1216436
10 M Crabb, I James, Fibrewise homotopy theory, Springer Monographs in Mathematics, Springer London Ltd. (1998) MR1646248
11 A Dold, Homology of symmetric products and other functors of complexes, Ann. of Math. (2) 68 (1958) 54–80 MR0097057
12 A Dold, R Thom, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. (2) 67 (1958) 239–281 MR0097062
13 B A Dubrovin, A T Fomenko, S P Novikov, Modern geometry—methods and applications. Part I, Graduate Texts in Mathematics 93, Springer (1992) MR1138462 The geometry of surfaces, transformation groups, and fields, Translated from the Russian by Robert G Burns
14 W Dwyer, M Weiss, B Williams, A parametrized index theorem for the algebraic K-theory Euler class, Acta Math. 190 (2003) 1–104 MR1982793
15 S Feder, The reduced symmetric product of projective spaces and the generalized Whitney theorem, Illinois J. Math. 16 (1972) 323–329 MR0296966
16 V V Gorjunov, Cohomology of braid groups of series C and D, Trudy Moskov. Mat. Obshch. 42 (1981) 234–242 MR622003
17 A Hatcher, Algebraic topology, Cambridge University Press (2002) MR1867354
18 S Kallel, Configuration spaces and the topology of curves in projective space, from: "Topology, geometry, and algebra: interactions and new directions (Stanford, CA, 1999)", Contemp. Math. 279, Amer. Math. Soc. (2001) 151–175 MR1850746
19 S Kallel, Spaces of particles on manifolds and generalized Poincaré dualities, Q. J. Math. 52 (2001) 45–70 MR1820902
20 S Kallel, R Karoui, Symmetric joins and weighted barycenters arXiv:math.AT/0602283
21 S Kallel, P Salvatore, work in progress on projective sigma models
22 S Kallel, P Salvatore, Symmetric products of two dimensional complexes, from: "Recent developments in algebraic topology", Contemp. Math. 407, Amer. Math. Soc. (2006) 147–161 MR2248976
23 D McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975) 91–107 MR0358766
24 R J Milgram, P Löffler, The structure of deleted symmetric products, from: "Braids (Santa Cruz, CA, 1986)", Contemp. Math. 78, Amer. Math. Soc. (1988) 415–424 MR975092
25 J Morava, The tangent bundle of an almost-complex free loopspace, Homology Homotopy Appl. 3 (2001) 407–415 MR1856034 Equivariant stable homotopy theory and related areas (Stanford, CA, 2000)
26 H R Morton, Symmetric products of the circle, Proc. Cambridge Philos. Soc. 63 (1967) 349–352 MR0210096
27 J Mostovoy, Geometry of truncated symmetric products and real roots of real polynomials, Bull. London Math. Soc. 30 (1998) 159–165 MR1489327
28 H Mùi, Duality in the infinite symmetric products, Acta Math. Vietnam. 5 (1980) MR627346
29 M Nakaoka, Cohomology of symmetric products, J. Inst. Polytech. Osaka City Univ. Ser. A 8 (1957) 121–145 MR0102069
30 F Napolitano, Configuration spaces on surfaces, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998) 887–892 MR1663485
31 F Napolitano, On the cohomology of configuration spaces on surfaces, J. London Math. Soc. (2) 68 (2003) 477–492 MR1994695
32 E Ossa, On the cohomology of configuration spaces, from: "Algebraic topology: new trends in localization and periodicity (Sant Feliu de Guíxols, 1994)", Progr. Math. 136, Birkhäuser (1996) 353–361 MR1397743
33 F Roth, On the category of euclidean configuration spaces, from: "Groups, homotopy and configuration spaces (Tokyo 2005)" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13 (2008) 447–461
34 P Salvatore, Configuration spaces on the sphere and higher loop spaces, Math. Z. 248 (2004) 527–540 MR2097373
35 G Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973) 213–221 MR0331377
36 G Segal, The topology of spaces of rational functions, Acta Math. 143 (1979) 39–72 MR533892
37 P A Smith, Manifolds with abelian fundamental groups, Ann. of Math. (2) 37 (1936) 526–533 MR1503296
38 R M Switzer, Counting elements in homotopy sets, Math. Z. 178 (1981) 527–554 MR638816
39 V A Vassiliev, Complements of discriminants of smooth maps: topology and applications, Translations of Mathematical Monographs 98, American Mathematical Society (1992) MR1168473 Translated from the Russian by B Goldfarb
40 C H Wagner, Symmetric, cyclic, and permutation products of manifolds, Dissertationes Math. (Rozprawy Mat.) 182 (1980) 52 MR605369
41 J Wang, On the braid groups for P² and the Mobius band, PhD thesis, University of Rochester (1997)
42 P J Welcher, Symmetric products and the stable Hurewicz homomorphism, Illinois J. Math. 24 (1980) 527–544 MR586793