Homological stability for over a local ring
Author:
Stanisław Betley
Journal:
Trans. Amer. Math. Soc. 303 (1987), 413429
MSC:
Primary 20G10; Secondary 11E72, 18G99, 19D55
MathSciNet review:
896030
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Abstract 
References 
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Additional Information
Abstract: Let be a local ring, a free module over of rank and a bilinear form on which has in some basis the matrix . Let be the group of automorphisms of which preserve . We prove the following theorem: if is big enough with respect to then the inclusion homomorphism induces an isomorphism .
 [Ba]
H. Bass, Algebraic theory, Benjamin, New York, 1968. MR 0249491 (40:2736)
 [Be]
S. Betley, Hyperbolic posets and homology stability for , J. Pure Appl. Algebra 43 (1986), 19. MR 862869 (88b:20066)
 [Bo]
A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. Ećole Norm. Sup. (4) 7 (1974), 235272. MR 0387496 (52:8338)
 [Ch]
R. Charney, Homology stability for of a Dedekind domain, Invent. Math. 56 (1980), 117. MR 557579 (81h:18010)
 [D]
W. G. Dwyer, Twisted homological stability for general linear groups, Ann. of Math. (2) 111 (1980), 239251. MR 569072 (81b:18006)
 [K]
W. Van der Kallen, Homology stability for linear group, Invent. Math. 60 (1980), 269295. MR 586429 (82c:18011)
 [M]
H. Maazen, Homology stability for the general linear group, Thesis, Univ. of Utrecht, 1979.
 [Q]
D. Quillen, MIT Lectures, 197475.
 [R]
A. A. Ranicki, Algebraic theory. I: Foundations, Proc. London Math. Soc. 27 (1973), 101125. MR 0414661 (54:2760a)
 [Sp]
E. H. Spanier, Algebraic topology, McGrawHill, New York, 1966. MR 0210112 (35:1007)
 [S]
A. A. Suslin, Stability in algebraic theory, Lecture Notes in Math., vol. 966, SpringerVerlag, Berlin and New York, 1982.
 [V1]
K. Vogtmann, Homological stability for , Comm. Algebra 7 (1979), 938. MR 514863 (81b:18005)
 [V2]
, Spherical posets and homology stability for , Topology 20 (1981), 119132. MR 605652 (82d:18016)
 [V3]
, A Stiefel complex for the orthogonal group of a field, Comment. Math. Helv. 57 (1982), 1121. MR 672842 (84b:18007)
 [W]
J. B. Wagoner, Stability for homology of the general linear group over a local ring, Topology 15 (1976), 417423. MR 0417263 (54:5320)
 [Ba]
 H. Bass, Algebraic theory, Benjamin, New York, 1968. MR 0249491 (40:2736)
 [Be]
 S. Betley, Hyperbolic posets and homology stability for , J. Pure Appl. Algebra 43 (1986), 19. MR 862869 (88b:20066)
 [Bo]
 A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. Ećole Norm. Sup. (4) 7 (1974), 235272. MR 0387496 (52:8338)
 [Ch]
 R. Charney, Homology stability for of a Dedekind domain, Invent. Math. 56 (1980), 117. MR 557579 (81h:18010)
 [D]
 W. G. Dwyer, Twisted homological stability for general linear groups, Ann. of Math. (2) 111 (1980), 239251. MR 569072 (81b:18006)
 [K]
 W. Van der Kallen, Homology stability for linear group, Invent. Math. 60 (1980), 269295. MR 586429 (82c:18011)
 [M]
 H. Maazen, Homology stability for the general linear group, Thesis, Univ. of Utrecht, 1979.
 [Q]
 D. Quillen, MIT Lectures, 197475.
 [R]
 A. A. Ranicki, Algebraic theory. I: Foundations, Proc. London Math. Soc. 27 (1973), 101125. MR 0414661 (54:2760a)
 [Sp]
 E. H. Spanier, Algebraic topology, McGrawHill, New York, 1966. MR 0210112 (35:1007)
 [S]
 A. A. Suslin, Stability in algebraic theory, Lecture Notes in Math., vol. 966, SpringerVerlag, Berlin and New York, 1982.
 [V1]
 K. Vogtmann, Homological stability for , Comm. Algebra 7 (1979), 938. MR 514863 (81b:18005)
 [V2]
 , Spherical posets and homology stability for , Topology 20 (1981), 119132. MR 605652 (82d:18016)
 [V3]
 , A Stiefel complex for the orthogonal group of a field, Comment. Math. Helv. 57 (1982), 1121. MR 672842 (84b:18007)
 [W]
 J. B. Wagoner, Stability for homology of the general linear group over a local ring, Topology 15 (1976), 417423. MR 0417263 (54:5320)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198708960304
PII:
S 00029947(1987)08960304
Keywords:
Spherical simplicial complex,
homology of a group
Article copyright:
© Copyright 1987
American Mathematical Society
