Alexandru Dimca
Arithmetic group symmetry and finiteness properties of Torelli groups.
Thu, 02/04/2010 - 16:01 — SomNambulAuthors: Alexandru Dimca, Stefan Papadima
Subjects: Group Theory
AbstractWe examine groups whose resonance varieties, characteristic varieties and
Sigma-invariants have a natural arithmetic group symmetry, and we explore
implications on various finiteness properties of subgroups. We compute
resonance varieties, characteristic varieties and Alexander polynomials of
Torelli groups, and we show that all subgroups containing the Johnson kernel
have finite first Betti number, when the genus is at least four.Quasi-K\"ahler groups, 3-manifold groups, and formality.
Thu, 01/07/2010 - 16:01 — SomNambulAuthors: Alexandru Dimca, Alexander I. Suciu, Stefan Papadima
Subjects: Algebraic Geometry
AbstractIn this note, we address the following question: Which 1-formal groups occur
as fundamental groups of both quasi-K\"ahler manifolds and closed, connected,
orientable 3-manifolds. We classify all such groups, at the level of Malcev
completions, and compute their coranks. Dropping the assumption on
realizability by 3-manifolds, we show that the corank equals the isotropy index
of the cup-product map in degree one. Finally, we examine the formality
properties of smooth affine surfaces and quasi-homogeneous isolated surface
singularities.First Milnor cohomology of hyperplane arrangements.
Fri, 08/21/2009 - 19:51 — SomNambulAuthors: Nero Budur, Alexandru Dimca, Morihiko Saito
Subjects: Algebraic Geometry
AbstractWe show a combinatorial formula for a lower bound of the dimension of the
non-unipotent monodromy part of the first Milnor cohomology of a hyperplane
arrangement satisfying some combinatorial conditions. This gives exactly its
dimension if a stronger combinatorial condition is satisfied. We also prove a
non-combinatorial formula for the dimension of the non-unipotent part of the
first Milnor cohomology, which apparently depends on the position of the
singular points. The latter generalizes a formula previously obtained by the
second named author.
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