On Thurston's construction of a surjective homomorphism $H_{2n+1}(B\Gamma_{n}, \mathbb{Z}) \to \mathbb{R}$

2018 ◽  
Author(s):  
Tadayoshi Mizutani
Keyword(s):  
Surjective Homomorphism

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 The complexity of surjective homomorphism problems—a survey

2012 ◽  
Vol 160 (12) ◽  
pp. 1680-1690 ◽  
Author(s):  
Manuel Bodirsky ◽  
Jan Kára ◽  
Barnaby Martin
Keyword(s):  
Surjective Homomorphism

Automatic Continuity of Homomorphisms in Non-associative Banach Algebras

2013 ◽  
Vol 65 (5) ◽  
pp. 989-1004
Author(s):  
C-H. Chu ◽  
M. V. Velasco
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Surjective Homomorphism ◽  
Automatic Continuity ◽  
Normed Algebra ◽  
Associative Algebras ◽  
Rare Element ◽  
Rare Elements

AbstractWe introduce the concept of a rare element in a non-associative normed algebra and show that the existence of such an element is the only obstruction to continuity of a surjective homomorphism from a non-associative Banach algebra to a unital normed algebra with simple completion. Unital associative algebras do not admit any rare elements, and hence automatic continuity holds.

scholarly journals The universal n-pointed surface bundle only has n sections

2019 ◽  
Vol 11 (02) ◽  
pp. 293-309 ◽  
Author(s):  
Lei Chen
Keyword(s):  
Fixed Points ◽  
Surjective Homomorphism ◽  
Independent Interest ◽  
Diffeomorphism Group ◽  
Classifying Space ◽  
Universal Bundle ◽  
Genus Formula ◽  
Surface Bundle ◽  
Hyperelliptic Surface

The classifying space BDiff[Formula: see text] of the orientation-preserving diffeomorphism group of a surface [Formula: see text] of genus [Formula: see text] fixing [Formula: see text] points pointwise has a universal bundle [Formula: see text] The [Formula: see text] fixed points provide [Formula: see text] sections [Formula: see text] of [Formula: see text]. In this paper we prove a conjecture of R. Hain that any section of [Formula: see text] is homotopic to some [Formula: see text]. Let [Formula: see text] be the space of ordered [Formula: see text]-tuple of distinct points on [Formula: see text]. As part of the proof of Hain’s conjecture, we prove a result of independent interest: any surjective homomorphism [Formula: see text] is equal to one of the forgetful homomorphisms [Formula: see text], possibly post-composed with an automorphism of [Formula: see text]. We also classify sections of the universal hyperelliptic surface bundle.

scholarly journals SAW*-ALGEBRAS ARE ESSENTIALLY NON-FACTORIZABLE

2014 ◽  
Vol 57 (1) ◽  
pp. 1-5 ◽  
Author(s):  
SAEED GHASEMI
Keyword(s):  
Tensor Product ◽  
Surjective Homomorphism ◽  
Infinite Dimensional ◽  
Calkin Algebra ◽  
C Algebras

AbstractIn this paper, we solve a question of Simon Wassermann, whether the Calkin algebra can be written as a C*-tensor product of two infinite dimensional C*-algebras. More generally, we show that there is no surjective *-homomorphism from a SAW*-algebra onto C*-tensor product of two infinite dimensional C*-algebras.

scholarly journals FINITE COVERS OF THE INFINITE CYCLIC COVER OF A KNOT

2009 ◽  
Vol 18 (01) ◽  
pp. 75-85
Author(s):  
J. O. BUTTON
Keyword(s):  
Finite Index ◽  
Commutator Subgroup ◽  
Surjective Homomorphism ◽  
Cyclic Cover ◽  
Finite Covers ◽  
Infinite Cyclic Cover ◽  
Simply Connected

We show that the commutator subgroup G′ of a classical knot group G need not have subgroups of every finite index, but it will if G′ has a surjective homomorphism to the integers and we give an exact criterion for that to happen. We also give an example of a knotted Sn in Sn+2 for all n ≥ 2 whose infinite cyclic cover is not simply connected but has no proper finite covers.

scholarly journals Deformations of rings

1989 ◽  
Vol 39 (3) ◽  
pp. 361-367
Author(s):  
Joe Yanik
Keyword(s):  
Local Ring ◽  
Complete Intersection ◽  
Surjective Homomorphism ◽  
Homological Dimension ◽  
Flat Extension

Let A and A0 be rings with a surjective homomorphism A → A0. Given a flat extension B0 of A0, a deformation of B0/A0 over A is a flat extension B of A such that B ⊗AA0 is isomorphic to B0. We show that such a deformation will exist if A0 is an Artin local ring, A is noetherian, and the homological dimension of B0 over A0 is ≤ 2. We also show that a deformation will exist if the kernel of A is nilpotent and if A0 is a finitely generted A0-algebra whose defining ideal is a local complete intersection.

Sign in / Sign up

Export Citation Format

Share Document