Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formality, Alexander invariants, and a question of Serre   We elucidate the key role played by formality in the theory of characteristic
and resonance varieties. We show that the I-adic completion of the Alexander
invariant of a 1-formal group G is determined solely by the cup-product map in
low degrees. It follows that the germs at the origin of the characteristic and
resonance varieties of G are analytically isomorphic; in particular, the
tangent cone to V_k(G) at 1 equals R_k(G). This provides new obstructions to
1-formality. A detailed analysis of the irreducible components of the tangent
cone at 1 to the first characteristic variety yields powerful obstructions to
realizing a finitely presented group as the fundamental group of a smooth,
complex quasi-projective algebraic variety. This sheds new light on a classical
problem of J.-P. Serre. Applications to arrangements, configuration spaces,
coproducts of groups, and Artin groups are given.

32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg