Related papers: Correction to: Reductions to simple fusion systems

In this note, a generalization of the Thompson transfer lemma and its various extensions, most recently due to Lyons, is proven in the context of saturated fusion systems. A strengthening of Alperin's fusion theorem is also given in this…

We introduce the notion of a pro-fusion system on a pro-p group, which generalizes the notion of a fusion system on a finite p-group. We also prove a version of Alperin's Fusion Theorem for pro-fusion systems.

We correct the proof of Theorem 4.1 from [C. R. Math. Acad. Sci. Soc. R. Can. \textbf{44} (2022), no. 4, 88--112].

G\"odel's argument for the First Incompleteness Theorem is, structurally, a proof by contradiction. This article intends to reframe the argument by, first, isolating an additional assumption the argument relies on, and then, second, arguing…

We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…

We present in this work a new and simple proof of the false centre theorem.

We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.

We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.

This is an erratum to an earlier paper, "Generalizations of the Poincar\'e-Birkhoff theorem." An error in the statement of one of the theorems is corrected.

We explain and correct a mistake in Section 2.6 and Appendix C of the first and second author's paper "Representation Growth and Rational Singularities of the Moduli Space of Local Systems" arXiv:1307.0371.

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.

Linking systems were introduced to provide algebraic models for $p$-completed classifying spaces of fusion systems. Every linking system over a saturated fusion system $\mathcal{F}$ corresponds to a group-like structure called a locality.…

This paper has been withdrawn by the authors due to a mistake in the proof of the chief result. In particular Theorem 1.3 is correct, while Theorem 1.1 and Theorem 1.2 hold with \mu>0 and a suitable restriction on the exponent p. The proof…

In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…

In this paper, we give a simple proof for the small cancellation conditions of the upper presentations of 2-bridge link groups, which holds the key to the proof of the main result of [1]. We also give an alternative proof of the main result…

In a recent paper, Amini et al. introduce a general framework to prove duality theorems between special decompositions and their dual combinatorial object. They thus unify all known ad-hoc proofs in one single theorem. While this…

The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.