Homology stability for orthogonal groups over algebraically closed fields

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1. [1] Betley S., Homology stability for $O(n,n)$ over a local ring, Trans. Amer. Math. Soc.303 (1987) 413-429. Zbl0632.20026MR896030
2. [2] Betley S., Homology stability for $O(n,n)$ over a semi-local ring, Glasgow Math. J.32 (1990) 255-259. Zbl0722.20031MR1058540
3. [3] Bökstedt M., Brun M., Dupont J., Homology of $O\left(n\right)$ and $O^1(1,n)$ made discrete: an application of edgewise subdivision, J. Pure Appl. Algebra123 (1998) 131-152. Zbl0910.20026MR1492898
4. [4] Borel A., Linear Algebraic Groups, Grad. Texts in Math., vol. 126, second revised ed., Springer-Verlag, 1991. Zbl0726.20030MR1102012
5. [5] Brown K.S., Cohomology of Groups, Grad. Texts in Math., vol. 87, Springer-Verlag, 1982. Zbl0584.20036MR672956
6. [6] Cathelineau J.-L., Homology of tangent groups considered as discrete groups and scissors congruences, J. Pure Appl. Algebra132 (1998) 9-25. Zbl0928.18006MR1634379
7. [7] Cathelineau J.-L., Scissors congruences and the bar and cobar constructions, J. Pure Appl. Algebra181 (2003) 141-179. Zbl1037.52012MR1975297
8. [8] Cathelineau J.-L., Projective configurations, homology of orthogonal groups and Milnor K-theory, Duke Math. J.121 (2004) 343-387. Zbl1057.19002MR2034645
9. [9] Cathelineau J.-L., Homology of orthogonal groups: a quadratic algebra, 30 (2003) 13-35. Zbl1047.18013MR2061846
10. [10] Cathelineau J.-L., The Pfaffian and the Lie algebra homology of skew-symmetric matrices, Math. Res. Let.11 (2004) 315-326. Zbl1060.17011MR2067476
11. [11] Charney R.M., A generalization of a theorem of Vogtmann, J. Pure Appl. Algebra44 (1987) 107-125. Zbl0615.20024MR885099
12. [12] Collinet G., Quelques propriétés homologiques du groupe $O_n\left(Z\right[1/2\left]\right)$, Thèse, Paris, 2002. 
13. [13] Dieudonné J., Sur les groupes classiques, Hermann, Paris, 1958. Zbl0926.20030MR344355
14. [14] Dupont J.L., Algebras of polytopes and homology of flag complexes, Osaka J. Math.19 (1982) 599-641. Zbl0499.51014MR676240
15. [15] Dupont J.L., Scissors Congruences, Group Homology and Characteristic Classes, Nankai Tracts in Mathematics, vol. 1, World Scientific, 2001. Zbl0977.52020MR1832859
16. [16] Dupont J.L., Sah C.H., Scissors congruences II, J. Pure Appl. Algebra25 (1982) 159-195. Zbl0496.52004MR662760
17. [17] Dupont J.L., Parry W., Sah C.H., Homology of classical Lie groups made discrete II, J. Algebra113 (1988) 215-260. Zbl0657.55022MR928063
18. [18] Friedlander E.M., Homology stability for classical groups over finite fields, in: Lecture Notes in Math., vol. 551, Springer-Verlag, 1976, pp. 290-302. Zbl0358.18013MR482741
19. [19] Guin D., Homologie du groupe linéaire et K-théorie de Milnor des anneaux, J. Algebra123 (1989) 27-59. Zbl0669.20037MR1000474
20. [20] Goncharov A., Volumes of hyperbolic manifolds and mixed Tate motives, J. Amer Math. Soc.12 (1999) 569-618. Zbl0919.11080MR1649192
21. [21] Hutchinson K., A new approach to Matsumoto's theorem, K-Theory4 (1990) 181-200. Zbl0725.19001MR1081659
22. [22] Van der Kallen W., Homology stability for linear groups, Invent. Math.60 (1980) 269-295. Zbl0415.18012MR586429
23. [23] Karoubi M., Théorie de Quillen et homologie du groupe orthogonal, Ann. of Math.112 (1980) 207-257. Zbl0478.18008MR592291
24. [24] Karoubi M., Le théorème fondamental de la K-théorie hermitienne, Ann. of Math.112 (1980) 259-282. Zbl0483.18008MR592292
25. [25] Lam T.Y., The Algebraic Theory of Quadratic Forms, Benjamin, 1973. Zbl0259.10019MR396410
26. [26] Loday J.L., Procesi C., Homology of symplectic and orthogonal algebras, Adv. in Math.69 (1988) 93-108. Zbl0716.17019MR937318
27. [27] Milnor J., Algebraic K-theory of quadratic forms, Invent. Math.9 (1970) 318-344. Zbl0199.55501MR260844
28. [28] Mirzaii B., Van der Kallen W., Homology stability for unitary groups, Doc. Math.7 (2002) 143-166. Zbl0999.19005MR1911214
29. [29] Nesterenko T.Y., Suslin A.A., Homology of the full linear group over a local ring and Milnor's K-theory, Math. SSSR Izvestija34 (1990) 121-145. Zbl0684.18001MR992981
30. [30] Panin I., Homological stabilization for the orthogonal and symplectic groups, J. Soviet Math.52 (1990) 3165-3170. Zbl0900.20077MR906859
31. [31] Panin I., On stabilization for orthogonal and symplectic algebraic K-theory, Leningrad Math. J.1 (1990) 741-764. Zbl0731.19003MR1015131
32. [32] Rosenberg J., Algebraic K-Theory and Its Applications, Grad. Text Math., vol. 147, Springer-Verlag, 1994. Zbl0801.19001MR1282290
33. [33] Sah C.H., Homology of classical Lie groups made discrete, I. Stability theorems and Schur multipliers, Comment. Math. Helv.61 (1986) 308-347. Zbl0607.57025MR856093
34. [34] Sah C.H., Hilbert's Third Problem: Scissors Congruence, Research Notes in Math., vol. 33, Pitman, 1979. Zbl0406.52004
35. [35] Sah C.H., Wagoner J.B., Second homology of Lie groups made discrete, Comm. Algebra5 (1977) 611-642. Zbl0375.18006MR646087
36. [36] Suslin A.A., Homology of ${\mathrm{GL}}_n$, characteristic classes and MilnorK-theory, in: Lecture Notes in Math., vol. 1046, Springer-Verlag, 1984, pp. 357-375. Zbl0528.18007MR750690
37. [37] Suslin A.A., Stability in algebraic K-theory, in: Oberwolfach, 1980, Lecture Notes in Math., vol. 966, Springer-Verlag, 1982, pp. 303-333. Zbl0498.18008MR689381
38. [38] Vogtman K., Homology stability for $O_{n,n}$, Comm. Algebra7 (1979) 9-38. Zbl0417.20040MR514863
39. [39] Vogtman K., Spherical posets and homology stability for $O_{n,n}$, Topology20 (1981) 119-132. Zbl0455.20031MR605652
40. [40] Vogtman K., A Stiefel complex for the orthogonal group of a field, Comment. Math. Helv.57 (1982) 11-21. Zbl0506.20018MR672842
41. [41] Weibel C., An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge Univ. Press, 1994. Zbl0834.18001MR1269324