@article{ASENS_2007_4_40_3_487_0,
author = {Cathelineau, Jean-Louis},
title = {Homology stability for orthogonal groups over algebraically closed fields},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {487--517},
year = {2007},
publisher = {Elsevier},
volume = {Ser. 4, 40},
number = {3},
doi = {10.1016/j.ansens.2007.03.001},
zbl = {1133.20037},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.ansens.2007.03.001/}
}
TY - JOUR AU - Cathelineau, Jean-Louis TI - Homology stability for orthogonal groups over algebraically closed fields JO - Annales scientifiques de l'École Normale Supérieure PY - 2007 SP - 487 EP - 517 VL - 40 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.ansens.2007.03.001/ DO - 10.1016/j.ansens.2007.03.001 LA - en ID - ASENS_2007_4_40_3_487_0 ER -
%0 Journal Article %A Cathelineau, Jean-Louis %T Homology stability for orthogonal groups over algebraically closed fields %J Annales scientifiques de l'École Normale Supérieure %D 2007 %P 487-517 %V 40 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.ansens.2007.03.001/ %R 10.1016/j.ansens.2007.03.001 %G en %F ASENS_2007_4_40_3_487_0
Cathelineau, Jean-Louis. Homology stability for orthogonal groups over algebraically closed fields. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 3, pp. 487-517. doi: 10.1016/j.ansens.2007.03.001
[1] , Homology stability for over a local ring, Trans. Amer. Math. Soc. 303 (1987) 413-429. | Zbl | MR
[2] , Homology stability for over a semi-local ring, Glasgow Math. J. 32 (1990) 255-259. | Zbl | MR
[3] , , , Homology of and made discrete: an application of edgewise subdivision, J. Pure Appl. Algebra 123 (1998) 131-152. | Zbl | MR
[4] , Linear Algebraic Groups, Grad. Texts in Math., vol. 126, second revised ed., Springer-Verlag, 1991. | Zbl | MR
[5] , Cohomology of Groups, Grad. Texts in Math., vol. 87, Springer-Verlag, 1982. | Zbl | MR
[6] , Homology of tangent groups considered as discrete groups and scissors congruences, J. Pure Appl. Algebra 132 (1998) 9-25. | Zbl | MR
[7] , Scissors congruences and the bar and cobar constructions, J. Pure Appl. Algebra 181 (2003) 141-179. | Zbl | MR
[8] , Projective configurations, homology of orthogonal groups and Milnor K-theory, Duke Math. J. 121 (2004) 343-387. | Zbl | MR
[9] , Homology of orthogonal groups: a quadratic algebra, 30 (2003) 13-35. | Zbl | MR
[10] , The Pfaffian and the Lie algebra homology of skew-symmetric matrices, Math. Res. Let. 11 (2004) 315-326. | Zbl | MR
[11] , A generalization of a theorem of Vogtmann, J. Pure Appl. Algebra 44 (1987) 107-125. | Zbl | MR
[12] Collinet G., Quelques propriétés homologiques du groupe , Thèse, Paris, 2002.
[13] , Sur les groupes classiques, Hermann, Paris, 1958. | Zbl | MR
[14] , Algebras of polytopes and homology of flag complexes, Osaka J. Math. 19 (1982) 599-641. | Zbl | MR
[15] , Scissors Congruences, Group Homology and Characteristic Classes, Nankai Tracts in Mathematics, vol. 1, World Scientific, 2001. | Zbl | MR
[16] , , Scissors congruences II, J. Pure Appl. Algebra 25 (1982) 159-195. | Zbl | MR
[17] , , , Homology of classical Lie groups made discrete II, J. Algebra 113 (1988) 215-260. | Zbl | MR
[18] , Homology stability for classical groups over finite fields, in: Lecture Notes in Math., vol. 551, Springer-Verlag, 1976, pp. 290-302. | Zbl | MR
[19] , Homologie du groupe linéaire et K-théorie de Milnor des anneaux, J. Algebra 123 (1989) 27-59. | Zbl | MR
[20] , Volumes of hyperbolic manifolds and mixed Tate motives, J. Amer Math. Soc. 12 (1999) 569-618. | Zbl | MR
[21] , A new approach to Matsumoto's theorem, K-Theory 4 (1990) 181-200. | Zbl | MR
[22] , Homology stability for linear groups, Invent. Math. 60 (1980) 269-295. | Zbl | MR
[23] , Théorie de Quillen et homologie du groupe orthogonal, Ann. of Math. 112 (1980) 207-257. | Zbl | MR
[24] , Le théorème fondamental de la K-théorie hermitienne, Ann. of Math. 112 (1980) 259-282. | Zbl | MR
[25] , The Algebraic Theory of Quadratic Forms, Benjamin, 1973. | Zbl | MR
[26] , , Homology of symplectic and orthogonal algebras, Adv. in Math. 69 (1988) 93-108. | Zbl | MR
[27] , Algebraic K-theory of quadratic forms, Invent. Math. 9 (1970) 318-344. | Zbl | MR
[28] , , Homology stability for unitary groups, Doc. Math. 7 (2002) 143-166. | Zbl | MR
[29] , , Homology of the full linear group over a local ring and Milnor's K-theory, Math. SSSR Izvestija 34 (1990) 121-145. | Zbl | MR
[30] , Homological stabilization for the orthogonal and symplectic groups, J. Soviet Math. 52 (1990) 3165-3170. | Zbl | MR
[31] , On stabilization for orthogonal and symplectic algebraic K-theory, Leningrad Math. J. 1 (1990) 741-764. | Zbl | MR
[32] , Algebraic K-Theory and Its Applications, Grad. Text Math., vol. 147, Springer-Verlag, 1994. | Zbl | MR
[33] , Homology of classical Lie groups made discrete, I. Stability theorems and Schur multipliers, Comment. Math. Helv. 61 (1986) 308-347. | Zbl | MR
[34] , Hilbert's Third Problem: Scissors Congruence, Research Notes in Math., vol. 33, Pitman, 1979. | Zbl
[35] , , Second homology of Lie groups made discrete, Comm. Algebra 5 (1977) 611-642. | Zbl | MR
[36] , Homology of , characteristic classes and Milnor K-theory, in: Lecture Notes in Math., vol. 1046, Springer-Verlag, 1984, pp. 357-375. | Zbl | MR
[37] , Stability in algebraic K-theory, in: Oberwolfach, 1980, Lecture Notes in Math., vol. 966, Springer-Verlag, 1982, pp. 303-333. | Zbl | MR
[38] , Homology stability for , Comm. Algebra 7 (1979) 9-38. | Zbl | MR
[39] , Spherical posets and homology stability for , Topology 20 (1981) 119-132. | Zbl | MR
[40] , A Stiefel complex for the orthogonal group of a field, Comment. Math. Helv. 57 (1982) 11-21. | Zbl | MR
[41] , An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge Univ. Press, 1994. | Zbl | MR
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