21 citations · 45 across the 8 of their papers we have counts for
8 papers · 1 filter
The loop linking number of line arrangements
Benoît Guerville-Ballé
In his Ph.D. thesis, Cadegan-Schlieper constructs an invariant of the embedded topology of a line arrangement which generalizes the -invariant introduced by Artal, Flo…
Ineffectiveness of homotopical invariants on Nakanishi's 4-move conjecture
Benoît Guerville-Ballé, Juan Viu-Sos
A -move is a local operation for links consisting in replacing two parallel arcs by four half twists. At the present time, it is not known if this induces an unkotting operation…
Topology and homotopy of lattice isomorphic arrangements
Benoît Guerville-Ballé
We prove the existence of lattice isomorphic line arrangements having -equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective…
Fundamental groups of real arrangements and torsion in the lower central series quotients
Enrique Artal Bartolo, Benoît Guerville-Ballé, Juan Viu-Sos
By using computer assistance, we prove that the fundamental group of the complement of a real complexified line arrangement is not determined by its intersection lattice, providing…
A linking invariant for algebraic curves
Benoît Guerville-Ballé, Jean-Baptiste Meilhan
We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. This invariant is shown to be a generaliz…
Multiplicativity of the -invariant and topology of glued arrangements
Benoît Guerville-Ballé
The invariant was first introduced by E. Artal, V. Florens and the author. Inspired by the idea of G. Rybnikov, we obtain a multiplicativity theorem…
An arithmetic Zariski 4-tuple of twelve lines
Benoît Guerville-Ballé
Using the invariant developed in [6], we differentiate four arrangements with the same combinatorial information but in different deformation classes. From these arrangements, we c…
A topological invariant of line arrangements
Enrique Artal Bartolo, Vincent Florens, Benoît Guerville-BallÉ
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arra…