Higher generation subgroup sets and the $ \Sigma $-invariants of graph groups

We present a general condition, based on the idea of n-generating subgroup sets, which implies that a given character represents a point in the homotopical or homological -invariants of the group G. Let be a finite simplicial graph, the flag complex induced by , and the graph group, or 'right angled Artin group', defined by . We use our result on n-generating subgroup sets to describe the homotopical and homological -invariants of in terms of the topology of subcomplexes of . In particular, this work determines the finiteness properties of kernels of maps from graph groups to abelian groups. This is the first complete computation of the -invariants for a family of groups whose higher invariants are not determined - either implicitly or explicitly - by ¹. Received: October 18, 1996     

Krichever Maps,Faà di Bruno Polynomials,and Cohomology in KP Theory

We study the geometrical meaning of the Faà di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faà di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.     

Geometry of Planes over Nonassociative Algebras

In this paper the geometric interpretation of the exceptional Lie groups F₄, E₆, E₇, and E₈ is given. These groups are groups of motions of elliptic hyperbolic planes over nonassociative algebras of octaves and split octaves and their tensor products with algebras of usual and split complex numbers, quaternions and octaves. The explicit expressions of motions of these planes and their figures of symmetry are presented.     

On polyhedral retracts and compactifications of locally symmetric spaces

The results in this paper are based on a previously constructed exhaustion of a locally symmetric space V=ΓX by Riemannian polyhedra, i.e., compact submanifolds with corners: V=_s0V(s). We show that the interior of every polyhedron V(s) is homeomorphic to V. The universal covering space X(s) of V(s) is quasi-isometric to the discrete group Γ. It can be written as the complement of a Γ-invariant union of horoballs in X (which in general have intersections giving rise to the corners). This yields exponential isoperimetric inequalities for Γπ₁(V(s)). We also discuss the relation of this compactification of V with the Borel–Serre compactification.     

Protection of the carbonyl groups in 1,2-indanedione: propellane versus acetal formation

The product resulting from the reaction between 1,2-indanedione and ethylene glycol under acidic catalysis is 2,5,7,10-tetraoxapropellane and not 1,2-dispirane as previously reported. Similar reactions also occur with 2-mercaptoethanol and 1,2-ethanedithiol, which form analogous propellanes and not corresponding thioacetals. This explains the difficulty of removing the protective groups under acidic conditions. These findings were corroborated by quantum chemical calculations. Under similar conditions, the longer-chain diol, 1,3-propyleneglycol and its thiol-analogue, 1,3-propanedithiol, form only mono-acetals, even when a 3-fold excess of the diol is applied. The nucleophilic attack, however, takes place at different positions: while propanedithiol forms the acetal at c-1, propylene glycol forms the acetal at c-2.     

Deficiencies of smooth manifolds

Being given a closed manifold Mⁿ, there are involutions (X²ⁿ, T) on closed manifolds of twice the dimension having fixed point set M. Kulkarni defined the deficiency of M for a class of involutions to be $\text{min}\text{(}\text{1}\text{2}\text{{}\text{dim}\text{H}{}^1\text{(X;Z}{}_{\mathrm{<mtext>2</mtext>}}\text{)?}\text{dim}\text{H}{}^1\text{(M;Z}{}_{\mathrm{<mtext>2</mtext>}}\text{)})}$ for all involutions (X, T) in the class. This paper exhibits manifolds for which the deficiency is positive for all involutions and studies the deficiencies for other classes.     

A conjecture of Abe-Iiyori and the Ree groups 2F4(q),Ⅱ

In this paper the author has solved a problem of Abe and liyori for the finite simple groups 2F4(q) and 2F4(2)'.     

Heterogeneity of OH Groups in H-Mordenites TPD and IR studies of ammonia desorption

We have investigated the temperature-programmed desorption (TPD) of ammonia during the activation of NH4Na-mordenites of different exchange degrees. Using a regularization method, desorption energy distribution functions have been calculated. The obtained results indicate the heterogeneity of the bridging Si-OH-Al groups in HNa-mordenites. This was concluded from the width of the distribution functions and from the presence of submaxima. For HNa-mordenites of exchange degrees below 50%, containing only hydroxyls in the broad channels, two distinct submaxima are present, thus suggesting the presence of at least two kinds of bridging hydroxyls of various acid strengths. In HNa-mordenites of exchange degrees above 50%, the hydroxyls appear in narrow channels and the distribution of ammonia desorption energy broadens on the side of higher energies. This may be related to a strong stabilization of ammonium ions inside narrow channels. The maximum concentrations of hydroxyls of desorption energies between 95 and 135 kJ mol_-1 and between 135 and 165 kJ mol_-1 calculated from TPD data were 3.9 and 3.3 OH per unit cell (u.c.). These values agree well with our previous IR results of concentrations of hydroxyls in broad and in narrow channels (3.7 and 2.8 OH per u.c.). The TPD data obtained for the heterogeneity of OH groups in HNa-mordenites are in accordance with the IR data concerning ammonia desorption. The IR band of OH groups restoring upon saturation of all the hydroxyls with ammonia and subsequent step-by-step desorption at increasing temperatures shifts to lower frequencies indicating that there are hydroxyls of various acid strengths and the less acidic hydroxyls restore first at lower desorption temperatures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Immobilization of the restriction endonuclease PstI

PstI has been immobilized in agarose. A solution of low melting agarose containing 1,6-hexamethylenediamine and PstI formed a gel that was effective in the linearization of pBR322 DNA. The gel containing PstI could be treated with 1,5-bis(N-acetylamino-N-succinimidoxy carbonyl)pentane, a crosslinking agent, without affecting the enzyme activity. Polymerization of acrylamide in presence of PstI led to conisderably reduced enzyme activity, although EcoRI under identical conditions showed high activity. It was found that acetylation of amino groups in PstI, by reaction with hydroxysuccinimide acetate, led to total inactivation of the enzyme activity. This reaction showed the presence of reactive amino groups that were essential for the enzyme activity of PstI. Involvement of these amino groups in binding to activated Sepharose 4B, during covalent immobilization, was responsible for inactive enzyme preparations.