Free and free abelian Euler–Satake characteristics of nonorientable 2-orbifolds

ar X iv : 0 90 2 . 22 20 v 1 [ m at h . D G ] 1 2 Fe b 20 09 CLASSIFYING CLOSED 2 - ORBIFOLDS WITH EULER CHARACTERISTICS

We determine the extent to which the collection of Γ-Euler-Satake characteristics classify closed 2-orbifolds. In particular, we show that the closed, connected, effective, orientable 2-orbifolds are classified by the collection of Γ-EulerSatake characteristics corresponding to free or free abelian Γ and are not classified by those corresponding to any finite collection of finitely generated di...

Intuitionistic Free Abelian Groups

Heterotic non–Abelian orbifolds

We perform the first systematic analysis of particle spectra obtained from heterotic string compactifications on non–Abelian toroidal orbifolds. After developing a new technique to compute the particle spectrum in the case of standard embedding based on higher dimensional supersymmetry, we compute the Hodge numbers for all recently classified 331 non–Abelian orbifold geometries which yield N = ...

Tachyon-Free Non-Supersymmetric Strings on Orbifolds

We discuss tachyon-free examples of (Type IIB on) non-compact nonsupersymmetric orbifolds with tachyons projected out by non-trivial discrete torsion. We also consider D3-branes in these backgrounds. The resulting non-supersymmetric gauge theories (including a chiral example) have supersymmetric spectra, but non-supersymmetric interactions. In the large N limit these theories are conformal to a...

Free abelian lattice-ordered groups

Let n be a positive integer and FA`(n) be the free abelian latticeordered group on n generators. We prove that FA`(m) and FA`(n) do not satisfy the same first-order sentences in the language L={+,−, 0,∧,∨} if m 6= n. We also show that Th(FA`(n)) is decidable iff n ∈ {1, 2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices. A. M. S. C...