arXiv subjects
Publications and source records attributed to Jure Kalisnik.
Given a smooth, open, oriented surface $X$ endowed with a family of complex structures $\{J_b\}_{b\in B}$ depending continuously on the parameter $b$ in a metrisable space $B$, we construct a continuous family of proper holomorphic maps $F_{b}:(X,J_b)\to\mathbb C^{2}$, $b\in B$.
The classical Serre-Swan's theorem defines a bijective correspondence between vector bundles and finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an etale Lie groupoid and the category of modules over its convolution algebra that are of finite type and of constant rank. Both of these constructions are functorially defined on the Morita bicategory of etale Lie groupoids and the given correspondence represents a natural equivalence between them.
Orbifold groupoids have been recently widely used to represent both effective and ineffective orbifolds. We show that every orbifold groupoid can be faithfully represented on a continuous family of finite dimensional Hilbert spaces. As a consequence we obtain the result that every orbifold groupoid is Morita equivalent to the translation groupoid of an action of a bundle of compact topological groups.