Generic trivializations of geometric theories

On the Gribov Problem for Generalized Connections

The bundle structure of the space A of Ashtekar’s generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the generic stratum. Its structure group equals the space G of all generalized gauge transforms modulo the constant center-valued gauge transforms. For abelian gauge th...

Nonholonomic Algebroids, Finsler Geometry, and Lagrange–Hamilton Spaces

We elaborate an unified geometric approach to classical mechanics, Riemann–Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N–connection) structure. There are investigated the conditions when the fundamental geometric objects like the anchor, metric and linear connection, almost sympletic and related almost complex structures may be canonically defined b...

Weakly one-based geometric theories

We study the class of weakly locally modular geometric theories introduced in [5], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We nd new conditions equivalent to weak local modularity: weak one-basedness and the absence of type de nable almost quasidesigns. Among other things, we show that weak one-basedness is closed under reducts and generic predi...

The Semistable Reduction Problem for the Space of Morphisms on P

We restate the semistable reduction theorem from geometric invariant theory in the context of spaces of morphisms from Pn to itself. For every complete curve C downstairs, we get a Pn-bundle on an abstract curve D mapping finite-to-one onto C, whose trivializations correspond to not necessarily complete curves upstairs with morphisms corresponding to identifying each fiber with the morphism the...

Fast Searching for Andrews-Curtis Trivializations