Following G. Laumon [12], to a nonramified `-adic local system E of rank n on a curve X one associates a complex of `-adic sheaves nKE on the moduli stack of rank n vector bundles on X with a section, which is cuspidal and satisfies the Hecke property for E. This is a geometric counterpart of the well-known construction due to J. Shalika [19] and I. Piatetski-Shapiro [18]. We express the cohomo...

The purpose of the paper is to study various aspects of star products on a symplectic manifold related to the Fedosov method. By introducing the notion of “quantum exponential maps”, we give a criterion characterizing Fedosov connections. As a consequence, a geometric realization is obtained for the equivalence between an arbitrary ∗-product and a Fedosov one. Every Fedosov ∗-product is shown t...

A new representation of 3D shape, referred to as Dynamic Shape Representation, is introduced in this paper. This representation is aimed at better supporting the generative application of shape grammars in product design. Inspired from real design process at a cognitive level, shape transforming actions in product design instead of geometric and topologic features of the product form are repres...

We formulate and prove a geometric version of the Fundamental Theorem of Algebraic K-Theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a nite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric...

Traditional methods of assessing the geometric integrity of any nely engineered product requires the use of xtures. The t is then tested with a feeler gauge. Fixtures are expensive to construct and transport and the degree of accuracy obtained may be insu cient, depending on the tolerance speci ed by the procurer of the part. In this paper, we discuss an alternative scienti c approach to assess...