41 research outputs found
Multiplicative Invariants and the Finite Co-Hopfian Property
A group is said to be, finitely co-Hopfian when it contains no proper subgroup of finite index isomorphic to itself. It is known that irreducible lattices in semisimple Lie groups are finitely co-Hopfian. However, it is not clear, and does not appear to be known, whether this property is preserved under direct product. We consider a strengthening of the finite co-Hopfian condition, namely the existence of a non-zero multiplicative invariant, and show that, under mild restrictions, this property is closed with respect to finite direct products. Since it is also closed with respect to commensurability, it follows that lattices in linear semisimple groups of general type are finitely co-Hopfian
Parallizable manifolds and the fundamental group
ntroduction. Low-dimensional topology is dominated by the fundamental group. However, since every finitely presented group is the fundamental group of some closed 4-manifold, it is often stated that the effective influence of π1 ends in dimension three. This is not quite true, however, and there are some interesting border disputes. In this paper, we show that, by imposing the extra condition of parallelizability on the tangent bundle, the dominion of π1 is extended by an extra dimension
Cancellation and stability properties of generalized torsion modules
Given a module
X
over a ring
Λ
its stability class consists of all modules
X
′
such that
X
⊕
Λ
a
≅
X
′
⊕
Λ
b
for some positive integers
a
,
b
. If the ring
Λ
is weakly finite then the stability class of a finitely generated
Λ
-module has the structure of a tree. We show that if, in addition,
X
is a generalized torsion module its stability class has the same shape as that of the zero module. In consequence we construct examples of nonprojective modules whose stability classes have arbitrarily large amounts of branching
Syzygies and diagonal resolutions for dihedral groups
We describe the syzygies of dihedral groups of order 4n+
Syzygies and Minimal Resolutions
The essence of linear algebra over a field resides in the fact that every vector space is free; that is, has a spanning set of linearly independent vectors. The study of linear algebra over more general rings attempts to approximate this situation by the method of free resolutions. When a module M is not free we make a first approximation to its being free by taking a surjective homomorphism ∊ : F0 → M where F0 is free to obtain an exact sequence
Diagonal resolutions for metacyclic groups
We show the finite metacyclic groups G(p, q) admit a class of projective resolutions which are periodic of period 2q and which in addition possess the properties that a) the differentials are 2×2 diagonal matrices; b) the Swan-Wall finiteness obstruction (cf [21], [22]) vanishes. We obtain thereby a purely algebraic proof of Petrie’s Theorem ([16])
that G(p, q) has free period 2q
Rings of Polynomials With Artinian Coefficients
We study the extent to which the weak Euclidewan and stably free cancellation properties hold for rings of Laurent polynomials with coefficients in an Artinian ring
Orientation and symmetries of Alexandrov spaces with applications in positive curvature
We develop two new tools for use in Alexandrov geometry: a theory of ramified
orientable double covers and a particularly useful version of the Slice Theorem
for actions of compact Lie groups. These tools are applied to the
classification of compact, positively curved Alexandrov spaces with maximal
symmetry rank.Comment: 34 pages. Simplified proofs throughout and a new proof of the Slice
Theorem, correcting omissions in the previous versio
Positive Selection Results in Frequent Reversible Amino Acid Replacements in the G Protein Gene of Human Respiratory Syncytial Virus
Human respiratory syncytial virus (HRSV) is the major cause of lower respiratory tract infections in children under 5 years of age and the elderly, causing annual disease outbreaks during the fall and winter. Multiple lineages of the HRSVA and HRSVB serotypes co-circulate within a single outbreak and display a strongly temporal pattern of genetic variation, with a replacement of dominant genotypes occurring during consecutive years. In the present study we utilized phylogenetic methods to detect and map sites subject to adaptive evolution in the G protein of HRSVA and HRSVB. A total of 29 and 23 amino acid sites were found to be putatively positively selected in HRSVA and HRSVB, respectively. Several of these sites defined genotypes and lineages within genotypes in both groups, and correlated well with epitopes previously described in group A. Remarkably, 18 of these positively selected tended to revert in time to a previous codon state, producing a “flip-flop” phylogenetic pattern. Such frequent evolutionary reversals in HRSV are indicative of a combination of frequent positive selection, reflecting the changing immune status of the human population, and a limited repertoire of functionally viable amino acids at specific amino acid sites