Homological stability for automorphism groups of free groups

1995 ◽  
Vol 70 (1) ◽  
pp. 39-62 ◽  
Author(s):  
Allen Hatcher
Keyword(s):  
Automorphism Groups ◽  
Free Groups ◽  
Homological Stability

scholarly journals Twisted homological stability for extensions and automorphism groups of free nilpotent groups

2014 ◽  
Vol 14 (1) ◽  
pp. 185-201 ◽  
Author(s):  
Markus Szymik
Keyword(s):  
General Result ◽  
Automorphism Groups ◽  
Free Groups ◽  
Nilpotent Groups ◽  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Polynomial Coefficients ◽  
Homological Stability

AbstractWe prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the general linear groups over the integers and the automorphism groups of free groups. The proof presented here uses a general result that applies to arbitrary extensions of groups, and that has other applications as well.

On the SL(2, C)-representation rings of free abelian groups

2018 ◽  
Vol 167 (02) ◽  
pp. 229-247
Author(s):  
TAKAO SATOH
Keyword(s):  
Abelian Group ◽  
Upper Bound ◽  
Automorphism Groups ◽  
Free Abelian Group ◽  
Abelian Groups ◽  
Free Groups ◽  
The Other ◽  
Subsequent Research ◽  
Representation Rings ◽  
Free Abelian Groups

AbstractIn this paper, we study “the ring of component functions” of SL(2, C)-representations of free abelian groups. This is a subsequent research of our previous work [11] for free groups. We introduce some descending filtration of the ring, and determine the structure of its graded quotients.Then we give two applications. In [30], we constructed the generalized Johnson homomorphisms. We give an upper bound on their images with the graded quotients. The other application is to construct a certain crossed homomorphisms of the automorphism groups of free groups. We show that our crossed homomorphism induces Morita's 1-cocycle defined in [22]. In other words, we give another construction of Morita's 1-cocyle with the SL(2, C)-representations of the free abelian group.

scholarly journals Assembling homology classes in automorphism groups of free groups

2016 ◽  
Vol 91 (4) ◽  
pp. 751-806 ◽  
Author(s):  
James Conant ◽  
Allen Hatcher ◽  
Martin Kassabov ◽  
Karen Vogtmann
Keyword(s):  
Automorphism Groups ◽  
Free Groups

scholarly journals EXTENDING REPRESENTATIONS OF BRAID GROUPS TO THE AUTOMORPHISM GROUPS OF FREE GROUPS

2005 ◽  
Vol 14 (08) ◽  
pp. 1087-1098 ◽  
Author(s):  
VALERIJ G. BARDAKOV
Keyword(s):  
Free Group ◽  
Braid Group ◽  
Automorphism Groups ◽  
Free Groups ◽  
Linear Representation ◽  
Braid Groups ◽  
Burau Representation ◽  
Pure Braid Group

We construct a linear representation of the group IA (Fn) of IA-automorphisms of a free group Fn, an extension of the Gassner representation of the pure braid group Pn. Although the problem of faithfulness of the Gassner representation is still open for n > 3, we prove that the restriction of our representation to the group of basis conjugating automorphisms Cbn contains a non-trivial kernel even if n = 2. We construct also an extension of the Burau representation to the group of conjugating automorphisms Cn. This representation is not faithful for n ≥ 2.

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