We derive polynomial identities of arbitrary degree n for syzygies degrees numerical semigroups $$S_m\!=\!\langle d_1,\ldots ,d_m\rangle $$ and show that $$n\ge m$$ they contain higher genera $$G_r\!=\!\sum _{s\in {\mathbb Z}_>\!\!\setminus S_m}s^ r$$ $$S_m$$ . find a number $$g_m\!=\!B_m-m+1$$ algebraically independent $$G_r$$ equations, related any $$g_m+1$$ genera, where $$B_m\!=\! \sum _{k=...

The theory of pseudodifferential operators and Fourier integral operators on compact manifolds is well established and their applications in mathematical physics well known , see for example Hörmander , Duistermaat , Treves 12 . For open (non compact) manifolds this is not the case, and that’s what I would like to focus on in this paper. We are interested in the geometry of the spaces of pseudo...

Gordon and Benson have proved that if a compact nilmanifold admits a Kahler structure then it is a torus [5] more precisely they proved that the condition (iv) fails for any symplectic structure on a non-toral nilmanifold M. This result was independently proved by Hasegawa [12] by showing that (v) fails for M. For a compact solvmanifold M of dimension 4 it is known that M has a Kahler structure...

We will say that a 3-manifold is almost compact if it can be obtained from a compact manifold N by removing a closed subset of dN. Then Theorem 1 is equivalent to the assertion that the universal covering of M is almost compact. A natural way to attempt to generalize Theorem 1 is to show that other coverings of M are almost compact. It was conjectured by Simon [Si] that if M is any compact P-ir...

Introduction. There has arisen in recent years a substantial body of work on “multiplier ideals” in commutative rings (see [La]). Multiplier ideals are integrally closed ideals with properties that lend themselves to highly interesting applications. One is tempted then to ask just how special multiplier ideals are among integrally closed ideals in general. In this note we show that in a two-dim...

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinan...