Volume 20, issue 6 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The cohomology rings of the unordered configuration spaces of elliptic curves

Roberto Pagaria

Algebraic & Geometric Topology 20 (2020) 2995–3012
DOI: 10.2140/agt.2020.20.2995
Bibliography
1 V I Arnold, The cohomology ring of the colored braid group, Mat. Zametki 5 (1969) 227 MR242196
2 V I Arnold, Certain topological invariants of algebraic functions, Tr. Mosk. Mat. Obs. 21 (1970) 27 MR0274462
3 S Ashraf, H Azam, B Berceanu, Representation theory for the Križ model, Algebr. Geom. Topol. 14 (2014) 57 MR3158753
4 H Azam, Cohomology groups of configuration spaces of Riemann surfaces, Bull. Math. Soc. Sci. Math. Roumanie 58(106) (2015) 33 MR3331058
5 O Bergvall, Cohomology of the toric arrangement associated with An, J. Fixed Point Theory Appl. 21 (2019) MR3894596
6 C Bibby, Cohomology of abelian arrangements, Proc. Amer. Math. Soc. 144 (2016) 3093 MR3487239
7 C F Bödigheimer, F R Cohen, Rational cohomology of configuration spaces of surfaces, from: "Algebraic topology and transformation groups" (editor T tom Dieck), Lecture Notes in Math. 1361, Springer (1988) 7 MR979504
8 C F Bödigheimer, F Cohen, L Taylor, On the homology of configuration spaces, Topology 28 (1989) 111 MR991102
9 F Callegaro, M D’Adderio, E Delucchi, L Migliorini, R Pagaria, Orlik–Solomon type presentations for the cohomology algebra of toric arrangements, Trans. Amer. Math. Soc. 373 (2020) 1909 MR4068285
10 C Chevalley, S Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948) 85 MR24908
11 F R Cohen, T J Lada, J P May, The homology of iterated loop spaces, 533, Springer (1976) MR0436146
12 P Deligne, Poids dans la cohomologie des variétés algébriques, from: "Proceedings of the International Congress of Mathematicians, I" (editor R D James), Canad. Math. Congress (1975) 79 MR0432648
13 G C Drummond-Cole, B Knudsen, Betti numbers of configuration spaces of surfaces, J. Lond. Math. Soc. 96 (2017) 367 MR3708955
14 C Dupont, The Orlik–Solomon model for hypersurface arrangements, Ann. Inst. Fourier (Grenoble) 65 (2015) 2507 MR3449588
15 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
16 Y Félix, D Tanré, The cohomology algebra of unordered configuration spaces, J. Lond. Math. Soc. 72 (2005) 525 MR2156668
17 W Fulton, J Harris, Representation theory: a first course, 129, Springer (1991) MR1153249
18 R Goodman, N R Wallach, Symmetry, representations, and invariants, 255, Springer (2009) MR2522486
19 M Goresky, R MacPherson, Stratified Morse theory, 14, Springer (1988) MR932724
20 B C Hall, Lie groups, Lie algebras, and representations : an elementary introduction, 222, Springer (2003) MR1997306
21 N Idrissi, The Lambrechts–Stanley model of configuration spaces, Invent. Math. 216 (2019) 1 MR3935037
22 B Knudsen, Betti numbers and stability for configuration spaces via factorization homology, Algebr. Geom. Topol. 17 (2017) 3137 MR3704255
23 I Kriz, On the rational homotopy type of configuration spaces, Ann. of Math. 139 (1994) 227 MR1274092
24 M Maguire, Computing cohomology of configuration spaces, preprint (2016) arXiv:1612.06314
25 J S Milne, Algebraic groups: the theory of group schemes of finite type over a field, 170, Cambridge Univ. Press (2017) MR3729270
26 F Napolitano, On the cohomology of configuration spaces on surfaces, J. Lond. Math. Soc. 68 (2003) 477 MR1994695
27 R Pagaria, Two examples of toric arrangements, J. Combin. Theory Ser. A 167 (2019) 389 MR3954076
28 P Salvatore, Configuration spaces on the sphere and higher loop spaces, Math. Z. 248 (2004) 527 MR2097373
29 C Schiessl, Betti numbers of unordered configuration spaces of the torus, preprint (2016) arXiv:1602.04748
30 B Totaro, Configuration spaces of algebraic varieties, Topology 35 (1996) 1057 MR1404924
31 C Voisin, Hodge theory and complex algebraic geometry, I, 76, Cambridge Univ. Press (2007) MR2451566
32 J H Wang, On the braid groups for P2, J. Pure Appl. Algebra 166 (2002) 203 MR1868546