Homology stability for classical regular semisimple varieties

2001 ◽  
Vol 236 (2) ◽  
pp. 251-290 ◽  
Author(s):  
G.I. Lehrer ◽  
G.B. Segal
Keyword(s):  
Homology Stability

scholarly journals Torsion classes in the cohomology of congruence subgroups

1989 ◽  
Vol 105 (2) ◽  
pp. 241-248 ◽  
Author(s):  
Dominique Arlettaz
Keyword(s):  
Prime Number ◽  
Congruence Subgroup ◽  
Surjective Homomorphism ◽  
Congruence Subgroups ◽  
Image Position ◽  
Homology Stability

For any prime number p, let Γn, p denote the congruence subgroup of SLn(ℤ) of level p, i.e. the kernel of the surjective homomorphism fp: SLn(ℤ) → SLn(p) induced by the reduction mod p (Fp is the field with p elements). We defineusing upper left inclusions Γn, p ↪ Γn+1, p. Recall that the groups Γn, p are homology stable with M-coefficients, for instance if M = ℚ, ℤ[1/p], or ℤ/q with q prime and q ╪ p: Hi(Γn, p; M) ≅ Hi(Γp; M) for n ≥ 2i + 5 from [7] (but the homology stability fails if M = ℤ or ℤ/p).

scholarly journals Homology stability for symmetric diffeomorphism and mapping class groups

2015 ◽  
Vol 160 (1) ◽  
pp. 121-139 ◽  
Author(s):  
ULRIKE TILLMANN
Keyword(s):  
Compact Manifold ◽  
Smooth Manifold ◽  
Mapping Class Groups ◽  
Mapping Class ◽  
Classifying Spaces ◽  
Class Groups ◽  
Connected Sum ◽  
Smooth Compact Manifold ◽  
Embedded Disks ◽  
Homology Stability

AbstractFor any smooth compact manifold W with boundary of dimension of at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of k points or k embedded disks (up to permutation) satisfy homology stability. The same is true for so-called symmetric diffeomorphisms of W connected sum with k copies of an arbitrary compact smooth manifold Q of the same dimension. The analogues for mapping class groups as well as other generalisations will also be proved.

Homology stability for 0n,n

1979 ◽  
Vol 7 (1) ◽  
pp. 9-38 ◽  
Author(s):  
Karen Vogtmann
Keyword(s):  
Homology Stability

Homology stability for linear groups

1980 ◽  
Vol 60 (3) ◽  
pp. 269-295 ◽  
Author(s):  
Wilberd van der Kallen
Keyword(s):  
Linear Groups ◽  
Homology Stability

scholarly journals Homology stability for unitary groups over S-arithmetic rings

2010 ◽  
Vol 8 (2) ◽  
pp. 293-322 ◽  
Author(s):  
G. Collinet
Keyword(s):  
Number Field ◽  
Strong Approximation ◽  
Ad Hoc ◽  
Approximation Theorem ◽  
Number Fields ◽  
Unitary Groups ◽  
Composition Algebra ◽  
Hermitian Forms ◽  
Homology Stability ◽  
Strong Approximation Theorem

AbstractWe prove that the homology of unitary groups over rings of S-integers in number fields stabilizes. Results of this kind are well known to follow from the high acyclicity of ad-hoc polyhedra. Given this, we exhibit two simple conditions on the arithmetic of hermitian forms over a ring A relatively to an anti-automorphism which, if they are satisfied, imply the stabilization of the homology of the corresponding unitary groups. When R is a ring of S-integers in a number field K, and A is a maximal R-order in an associative composition algebra F over K, we use the strong approximation theorem to show that both of these properties are satisfied. Finally we take a closer look at the case of On(ℤ[½]).

scholarly journals Tethers and homology stability for surfaces

2017 ◽  
Vol 17 (3) ◽  
pp. 1871-1916 ◽  
Author(s):  
Allen Hatcher ◽  
Karen Vogtmann
Keyword(s):  
Homology Stability
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