647 research outputs found
Piecewise principal comodule algebras
A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra PcoH. We prove that principality is a piecewise property: given N comodule-algebra surjections P → P_i whose kernels intersect to zero, P is principal if and only if all P_i’s are principal. Furthermore, assuming the principality of P, we show that the lattice these kernels generate is distributive if and only if so is the lattice obtained by intersection with PcoH. Finally, assuming the above distributivity property, we obtain a flabby sheaf of principal comodule algebras over a certain space that is universal for all such
N-families of surjections P → P_i and such that the comodule algebra of global sections is P
Non-homeomorphic topological rank and expansiveness
Downarowicz and Maass (2008) have shown that every Cantor minimal
homeomorphism with finite topological rank is expansive. Bezuglyi,
Kwiatkowski and Medynets (2009) extended the result to non-minimal cases. On
the other hand, Gambaudo and Martens (2006) had expressed all Cantor minimal
continuou surjections as the inverse limit of graph coverings. In this paper,
we define a topological rank for every Cantor minimal continuous surjection,
and show that every Cantor minimal continuous surjection of finite topological
rank has the natural extension that is expansive
On the connection between fundamental groups and pencils with multiple fibers
We present two results about the relationship between fundamental groups of
quasiprojective manifolds and linear systems on a projectivization. We prove
the existence of a plane curve with non-abelian fundamental group of the
complement which does not admit a mapping onto an orbifold with non-abelian
fundamental group. We also find an affine manifold whose irreducible components
of its characteristic varieties do not come from the pull-back of the
characteristic varieties of an orbifold
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