Given a Heegaard splitting of a three-manifold Y , we consider the SL(2,C) character variety of the Heegaard surface, and two complex Lagrangians associated to the handlebodies. We focus on the smooth open subset corresponding to irreducible representations. On that subset, the intersection of the Lagrangians is an oriented d-critical locus in the sense of Joyce. Bussi associates to such an int...

Let g be a complex semisimple Lie algebra, and f : g → G\\g the adjoint quotient map. Springer theory of Weyl group representations can be seen as the study of the singularities of f . In this paper, we give a generalization of Springer theory to visible, polar representations. It is a class of rational representations of reductive groups over C, for which the invariant theory works by analogy ...

In the framework of Abstract Differential Geometry, especially that dealing with vector sheaves (as expounded in [8]) and principal sheaves (initiated by [9]), we show that to a given principal sheaf (P ,G,X, π) together with a representation φ : G → GL(n,A), we associate a vector sheaf (E ,X, p). If φ is compatible with the representations of G and GL(n,A) into appropriate sheaves of Lie algeb...

It was shown in papers of Dosi and a recent article the author that there is sheaf Frechet-Arens-Michael algebras (locally solvable complex case polynomial growth real) on character space nilpotent Lie algebra. For algebra group affine transformations line (the simplest non-nilpotent algebra) we construct analogous sheaves non-commutative smooth holomorphic functions special set representations.

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

Let X ⊂ PdK be Drinfeld’s upper half space over a finite extension K of Qp. We construct for every GLd+1-equivariant vector bundle F on PdK , a GLd+1(K)equivariant filtration by closed subspaces on the K-Fréchet H(X ,F). This gives rise by duality to a filtration by locally analytic GLd+1(K)-representations on the strong dual H(X ,F). The graded pieces of this filtration are locally analytic in...

Let X ⊂ PdK be Drinfeld’s upper half space over a finite extension K of Qp. We construct for every GLd+1-equivariant vector bundle F on PdK , a GLd+1(K)equivariant filtration by closed subspaces on the K-Fréchet H(X ,F). This gives rise by duality to a filtration by locally analytic GLd+1(K)-representations on the strong dual H(X ,F). The graded pieces of this filtration are locally analytic in...

Let X ⊂ PK be Drinfeld’s upper half space over a finite extension K of Qp. We construct for every GLd+1-equivariant vector bundle F on PK , a GLd+1(K)equivariant filtration by closed subspaces on the K-Fréchet H0(X ,F). This gives rise by duality to a filtration by locally analytic GLd+1(K)-representations on the strong dual H0(X ,F)′. The graded pieces of this filtration are locally analytic i...