40,973 research outputs found
Gauge theory and Rasmussen's invariant
A previous paper of the authors' contained an error in the proof of a key
claim, that Rasmussen's knot-invariant s(K) is equal to its gauge-theory
counterpart. The original paper is included here together with a corrigendum,
indicating which parts still stand and which do not. In particular, the
gauge-theory counterpart of s(K) is not additive for connected sums.Comment: This version bundles the original submission with a 1-page
corrigendum, indicating the error. The new version of the corrigendum points
out that the invariant is not additive for connected sums. 23 pages, 3
figure
A note on the fermentation characteristics of red clover silage in response to advancing stage of maturity in the primary growth Corrigendum
Corrigendum to Irish Journal of Agricultural and Food Research, Volume 51, Number 1, 2012, pages 79–84. Available at http://hdl.handle.net/11019/324Corrigendu
Elliptic curves with a given number of points over finite fields
Given an elliptic curve and a positive integer , we consider the
problem of counting the number of primes for which the reduction of
modulo possesses exactly points over . On average (over a
family of elliptic curves), we show bounds that are significantly better than
what is trivially obtained by the Hasse bound. Under some additional
hypotheses, including a conjecture concerning the short interval distribution
of primes in arithmetic progressions, we obtain an asymptotic formula for the
average.Comment: A mistake was discovered in the derivation of the product formula for
K(N). The included corrigendum corrects this mistake. All page numbers in the
corrigendum refer to the journal version of the manuscrip
Spectral rigidity of automorphic orbits in free groups
It is well-known that a point in the (unprojectivized)
Culler-Vogtmann Outer space is uniquely determined by its
\emph{translation length function} . A subset of a
free group is called \emph{spectrally rigid} if, whenever
are such that for every then in . By
contrast to the similar questions for the Teichm\"uller space, it is known that
for there does not exist a finite spectrally rigid subset of .
In this paper we prove that for if is a subgroup
that projects to an infinite normal subgroup in then the -orbit
of an arbitrary nontrivial element is spectrally rigid. We also
establish a similar statement for , provided that is not
conjugate to a power of .
We also include an appended corrigendum which gives a corrected proof of
Lemma 5.1 about the existence of a fully irreducible element in an infinite
normal subgroup of of . Our original proof of Lemma 5.1 relied on a
subgroup classification result of Handel-Mosher, originally stated by
Handel-Mosher for arbitrary subgroups . After our paper was
published, it turned out that the proof of the Handel-Mosher subgroup
classification theorem needs the assumption that be finitely generated. The
corrigendum provides an alternative proof of Lemma~5.1 which uses the
corrected, finitely generated, version of the Handel-Mosher theorem and relies
on the 0-acylindricity of the action of on the free factor complex
(due to Bestvina-Mann-Reynolds). A proof of 0-acylindricity is included in the
corrigendum.Comment: Included a corrigendum which gives a corrected proof of Lemma 5.1
about the existence of a fully irreducible element in an infinite normal
subgroup of of Out(F_N). Note that, because of the arXiv rules, the
corrigendum and the original article are amalgamated into a single pdf file,
with the corrigendum appearing first, followed by the main body of the
original articl
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