We compute a twisted first cohomology group of the automorphism group of a free group with coefficients in the abelianization V of the IA-automorphism group of a free group. In particular, we show that it is generated by two crossed homomorphisms constructed with the Magnus representation and the Magnus expansion due to Morita and Kawazumi respectively. As a corollary, we see that the first Joh...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

The set of homology cobordisms from a surface to itself with markings of their boundaries has a natural monoid structure. To investigate the structure of this monoid, we define and study its Magnus representation and Reidemeister torsion invariants by generalizing Kirk-Livingston-Wang’s argument over the Gassner representation of string links. Moreover, by applying Cochran and Harvey’s framewor...

Background and Purpose: Cryptococcus. magnus is a non-Cryptococcus neoformans species isolated from certain plants, soil, air, and arctic glaciers. Case report: This report describes a case of a 23-year-old Iranian female with pruritus and vaginal irritation. Conventional tests and molecular analysis of the samples of vaginal discharge were performed. The mentioned analyses revealed Cryptoc...

In this paper, we study a series of L-torsion invariants from the viewpoint of the mapping class group of a surface. We establish some vanishing theorems for them. Moreover we explicitly calculate the first two invariants and compare them with hyperbolic volumes. 1. Magnus representation Let Σg,1 be a compact oriented smooth surface of genus g with a boundary ∂Σg,1 ∼= S . In this paper, we alwa...

Consider the kernel Magg of the Magnus representation of the Torelli group and the kernel Burn of the Burau representation of the braid group. We prove that for g ≥ 2 and for n ≥ 6 the groups Magg and Burn have infinite rank first homology. As a consequence we conclude that neither group has any finite generating set. The method of proof in each case consists of producing a kind of “Johnson-typ...