1,501 research outputs found
Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator
A group obtained from a nontrivial group by adding one generator and one
relator which is a proper power of a word in which the exponent-sum of the
additional generator is one contains the free square of the initial group and
almost always (with one obvious exception) contains a non-abelian free
subgroup. If the initial group is involution-free or the relator is at least
third power, then the obtained group is SQ-universal and relatively hyperbolic
with respect to the initial group.Comment: 11 pages. A Russian version of this paper is at
http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V3:
revised following referee's comment
Stability and Unobstructedness of Syzygy Bundles
It is a longstanding problem in Algebraic Geometry to determine whether the
syzygy bundle on \PP^N defined as the kernel of a general
epimorphism \xymatrix{\phi:\cO(-d_1)\oplus...\oplus\cO(-d_n)\ar[r] &\cO} is
(semi)stable. In this note, we restrict our attention to the case of syzygy
bundles on \PP^N associated to generic forms of the same degree . Our first goal is to prove that
is stable if . This bound improves,
in general, the bound given by G. Hein in \cite{B}, Appendix A.
In the last part of the paper, we study moduli spaces of stable rank
vector bundles on \PP^N containing syzygy bundles. We prove that if and , then the syzygy bundle is
unobstructed and it belongs to a generically smooth irreducible component of
dimension , if , and
, if N=2.Comment: 32 pages, minor change
The Kervaire-Laudenbach conjecture and presentations of simple groups
The statement ``no nonabelian simple group can be obtained from a nonsimple
group by adding one generator and one relator"
1) is equivalent to the Kervaire--Laudenbach conjecture;
2) becomes true under the additional assumption that the initial nonsimple
group is either finite or torsion-free.
Key words: Kervaire--Laudenbach conjecture, relative presentations, simple
groups, car motion, cocar comotion.
AMS MSC: 20E32, 20F05, 20F06.Comment: 20 pages, 13 figure
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