Alexander I. Suciu
Resonance varieties and Dwyer-Fried invariants.
Tue, 11/22/2011 - 15:01 — SomNambulAuthors: Alexander I. Suciu
Subjects: Algebraic Geometry
AbstractThe Dwyer-Fried invariants of a finite cell complex X are the subsets
\Omega^i_r(X) of the Grassmannian of r-planes in H^1(X,\Q) which parametrize
the regular \Z^r-covers of X having finite Betti numbers up to degree i. In
previous work, we showed that each \Omega-invariant is contained in the
complement of a union of Schubert varieties associated to a certain subspace
arrangement in H^1(X,\Q). Here, we identify a class of spaces for which this
inclusion holds as equality.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.Fundamental groups, Alexander invariants, and cohomology jumping loci.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Alexander I. Suciu
Subjects: Geometric Topology
AbstractWe survey the cohomology jumping loci and the Alexander-type invariants
associated to a space, or to its fundamental group. Though most of the material
is expository, we provide new examples and applications, which in turn raise
several questions and conjectures.Fundamental groups, Alexander invariants, and cohomology jumping loci.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Alexander I. Suciu
Subjects: Geometric Topology
AbstractWe survey the cohomology jumping loci and the Alexander-type invariants
associated to a space, or to its fundamental group. Though most of the material
is expository, we provide new examples and applications, which in turn raise
several questions and conjectures.
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