Related papers: Correction to: Reductions to simple fusion systems
The purpose of this note is to point to a gap in an argument in our paper "Stabilization for the automorphisms of free groups with boundaries", and explain how to fill it.
The ancillary file Corrigendum.pdf contains an explanation why our proof does not work.
We give a simple proof of a crucial lemma that is established in [1, Lemma 2.1] by induction, and plays important roles in that paper and [2].
We present a version of a proof by Andy Chermak of the existence and uniqueness of centric linking systems associated to arbitrary saturated fusion systems. This proof differs from the one by Chermak in that it is based on the computation…
We define a `tree of fusion systems' and give a sufficient condition for its completion to be saturated. We apply this result to enlarge an arbitrary fusion system by extending the automorphism groups of certain of its subgroups.
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
This note corrects some omissions in section 2 of the paper "Lipschitz connectivity and filling invariants in solvable groups and buildings."
We show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of a recent algorithm of A. Salagean.
We give a counterexample to Theorem 9 in [T.K. Subrahmonian Moothathu, Syndetically proximal pairs, J. Math. Anal. Appl. 379 (2011) 656--663]. We also provide sufficient conditions for the conclusion of Theorem 9 to hold.
We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…
We continue the work of [5] and [3], in which are considered papers in the literature that discuss fixed point assertions in digital topology. We discuss published assertions that are incorrect or incorrectly proven; that are severely…
We give down-to-earth proofs of the structure theorems for persistence modules.
We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
Due to the omission of a hypothesis from an elementary lemma in the author's paper "Gleason parts and point derivations for uniform algebras with dense invertible group", some of the proofs presented in that paper are flawed. We prove here…
This proof of Godel's first incompleteness theorem doesn't require omega-consistency, nor does it refer to codes of negated sentences as in Rosser's. It begins from where Godel's usual proof ends, and stalks it till it ends proving it.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We address two errors made in our paper arXiv:1511.03423. The most significant error is in Theorem 1.1. We repair this error, and show that the main result, Theorem 2.5 of arXiv:1511.03423, is true. The second error is in one of our…
We provide some corrections and clarifications to the paper [Gr3] of the title. In particular, we clarify the "left/right" conventions on complex reflection groups and their braid groups. Most importantly, we fill in a gap related to the…
We propose a slight correction and a slight improvement on the main result contained in "A lecture on Classical KAM Theorem" by J. P{\"o}schel.
We settle the fusion product decomposition theorem for higher-level affine Demazure modules for the cases $E^{(1)}_{6, 7, 8}, F^{(1)}_4$ and $E^{(2)}_{6}$, thus completing the main theorems of Chari et al. (J. Algebra, 2016) and Kus et al.…