On conformal manifolds of even dimension n ≥ 4 we construct a family of new conformally invariant differential complexes, each containing one coboundary operator of order greater than 1. Each bundle in each of these complexes appears either in the de Rham complex or in its dual (which is a different complex in the non-orientable case). Each of the new complexes is elliptic in case the conformal...

A conformal partition function Pm n (s), which arised in the theory of Diophantine equations supplemented with additional restrictions, is concerned also with the reciprocal and skew-reciprocal algebraic equations based on the polynomial invariants of the symmetric group Sn. Making use of the relationship between Gaussian generating function for conformal partitions and Molien generating functi...

Let M be a compact manifold with a spin structure χ and a Riemannian metric g. Let λ2g be the smallest eigenvalue of the square of the Dirac operator with respect to g and χ. The τ -invariant is defined as τ(M,χ) := sup inf q λ2gVol(M, g) 1/n where the supremum runs over the set of all conformal classes on M , and where the infimum runs over all metrics in the given class. We show that τ(T , χ)...

The main limitations of string field theory arise because its present formulation requires a background representing a classical solution, a background defined by a strictly conformally invariant theory. Here we sketch a construction for a gauge-invariant string field action around non-conformal backgrounds. The construction makes no reference to any conformal theory. Its two-dimensional field-...

This paper gives applications of earlier work of the authors on the use of expansion complexes for studying conformality of finite subdivision rules. The first application is that a one-tile rotationally invariant finite subdivision rule (with bounded valence and mesh approaching 0) has an invariant conformal structure, and hence is conformal. The paper next considers one-tile single valence fi...