Topological criteria for schlichtness

We give two sufficient criteria for schlichtness of envelopes of holomorphy in terms of topology. These are weakened converses of results of Kerner and Royden. Our first criterion generalizes a result of Hammond in dimension 2. Along the way we also prove a generalization of Royden's theorem.Comment: v2: 3 pages; added new results, including generalization of a theorem of Royde

Eliashberg's proof of Cerf's theorem

Following a line of reasoning suggested by Eliashberg, we prove Cerf's theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To this end we develop a moduli-theoretic version of Eliashberg's filling-with-holomorphic-discs method.Comment: 32 page

Uniform approximation of homeomorphisms by diffeomorphisms

We prove that a compactly supported homeomorphism of a smooth manifold of dimension greater or equal to 5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given homeomorphism is in addition volume preserving, then it can be approximated uniformly by volume preserving diffeomorphisms.Comment: v4: 5 pages; long overdue revision; clarified and improved statements, notation, and proofs. The main theorem may already be known, but I have not been able to find a precise reference. After talking to a number of topologists without getting a satisfactory answer, I decided to write up the proof myself. Comments and references welcom

Mean Dimension & Jaworski-type Theorems

According to the celebrated Jaworski Theorem, a finite dimensional aperiodic dynamical system $(X,T)$ embeds in the $1$-dimensional cubical shift $([0,1]^{\mathbb{Z}},shift)$. If $X$ admits periodic points (still assuming $\dim(X)<\infty$) then we show in this paper that periodic dimension $perdim(X,T)<\frac{d}{2}$ implies that $(X,T)$ embeds in the $d$-dimensional cubical shift $(([0,1]^{d})^{\mathbb{Z}},shift)$. This verifies a conjecture by Lindenstrauss and Tsukamoto for finite dimensional systems. Moreover for an infinite dimensional dynamical system, with the same periodic dimension assumption, the set of periodic points can be equivariantly immersed in $(([0,1]^{d})^{\mathbb{Z}},shift)$. Furthermore we introduce a notion of markers for general topological dynamical systems, and use a generalized version of the Bonatti-Crovisier tower theorem, to show that an extension $(X,T)$ of an aperiodic finite-dimensional system whose mean dimension obeys $mdim(X,T)<\frac{d}{16}$ embeds in the $(d+1)$-cubical shift $(([0,1]^{d+1})^{\mathbb{Z}},shift)$.Comment: To appear in Proceedings of the London Mathematical Societ

A rapid, easy and economical method for assay of drug resistance in Neurospora

Assay of bacterial drug resistance with linear concentration diffusion gradient plates was first described by Szylbalski (1952 Science 116:46-51). We have applied the method to Neurospora

Selection of improved microconidial strains of N. crassa

Selection of improved microconidial strain

Histochemical detection of the secretion of superoxide radicals and hydrogen peroxide by age-1 mutants of Neurospora

The Age-1 gene family consists of 16 functionally redundant, closely linked loci on linkage group I. (Munkres 1985 Superoxide Dismutases, Vol. III, CRC Press, Boca Raton, FL). Dominant mutations at those loci reduce conidial lifespan (loc. cit.) and cause multiple deficiencies of at least 12 antioxidant enzymes; the endocellular superoxide dismutases (SOD), and exocellular cell wall bound SOD isozyme, catalase, peroxidases and reductases (Munkres et al. 1984 Mech. Age. Dev. 24:83-100; Munkres 1990 Free Radical Bio. Med., in press). Colonies of the mutants secrete superoxide radicals and H2O2, apparently as a consequence of their antioxidant enzyme deficiencies. The purpose of this note is to describe histochemical methods that detect the secretions

An assay procedure for Neurospora malate deydrogenase

An assay procedure for Neurospora malate deydrogenas

Triangulation of the map of a GG-manifold to its orbit space

Let $G$ be a Lie group and $M$ a smooth proper $G$-manifold. Let $pi:Mto M/G$ denote the natural map to the orbit space. Then there exist a PL manifold $P$, a polyhedron $L$ and homeomorphisms $tau:Pto M$ and $\sigma:M/Gto L$ such that \sigma\circpi\circ\tau is PL. If $M$ and the $G$-action are of analytic class, we can choose subanalytic $\tau$ and then unique $P$ and $L$