III. Homonuclear Diatomics: Second-Row Elements 14 A. The diatomic boron molecule 16 1. Σg state 16 2. Σg state 19 B. The diatomic oxygen and carbon molecules in their lowest states 20 1. O2 20 2. Reflection symmetry 21 3. Electron repulsion 23 4. MCSCF calculations for O2 24 5. The C2 molecule 25 C. Spectroscopic notation for diatomic molecules 28 D. States of other homonuclear diatomic molecu...

We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under some mild topological assumptions, to a Gaussian fermionic system. In particular, for manifolds topologically equivalent to Σg × IR with Σg a closed and oriented Riemann surface of genus g, the corresponding 2+1-dimensional Euclidean quantum gravity may be related to the 3D-lattice Ising model before its thermodynamic l...

We present a formula expressing Earle’s twisted 1-cocycle on the mapping class group of a closed oriented surface of genus ≥ 2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita’s twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class...

We present a formula expressing Earle’s twisted 1-cocycle on the mapping class group of a closed oriented surface of genus ≥ 2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita’s twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class...

We apply the stellar population synthesis code by Cid Fernandes et al. to model the stellar contribution for a sample of 209 type II AGNs at redshifts 0.3 < z < 0.83 from the Sloan Digital Sky Survey. The reliable stellar velocity dispersions (σ∗) are obtained for 33 type II AGNs with significant stellar absorption features. According to the L[OIII] criterion of 3 × 10 L , 20 of which can be cl...

Let Σg → E → Σh be a surface bundle over a surface with monodromy representation ρ : π1Σh → Mod(Σg) contained in the Torelli group Ig. In this paper we express the cup product structure in H∗(E,Z) in terms of the Johnson homomorphism τ : Ig → ∧(H1(Σg ,Z)). This is applied to the question of obtaining an upper bound on the maximal n such that p1 : E → Σh1 , . . . , pn : E → Σhn are fibering maps...

Let G be a finite group, and let XG = {x = (x(s,t)) ∈ GZ 2 | x(s,t) = x(s,t−1) · x(s+1,t−1) for all (s, t) ∈ Z}. The compact zero–dimensional set XG carries a natural shift Z2–action σG and the pair ΣG = ( XG, σ G ) is a two–dimensional topological Markov shift. Using recent work by Crandall, Dilcher and Pomerance on the Fermat quotient, we show the following: if G is abelian, and the order of ...

We consider classical Teichmüller theory and the geodesic flow on the cotangent bundle of the Teichmüller space. We show that the corresponding orbits provide a canonical description of certain (2+1) gravity systems in which a set of point-like particles evolve in universes with topology Σg × R I where Σg is a Riemann surface of genus g > 1 . We construct an explicit York’s slicing presentation...

Let Γg be the fundamental group of a closed oriented Riemann surface Σg, g ≥ 2, and let G be a simple Lie group of Hermitian type. The Toledo invariant defines the subset of maximal representations Repmax(Γg , G) in the representation variety Rep(Γg , G). Repmax(Γg, G) is a union of connected components with similar properties as Teichmüller space T (Σg) = Repmax(Γg , PSL(2, R)). We prove that ...