Invariants of combinatorial line arrangements and Rybnikov's example

Following the general strategy proposed by G.Rybnikov, we present a proof of his well-known result, that is, the existence of two arrangements of lines having the same combinatorial type, but nonisomorphic fundamental groups. To do so, the Alexander Invariant and certain invariants of combinatorial...

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Detalles Bibliográficos
Autores: Artal Bartolo, Enrique, Carmona Ruber, Jorge, Cogolludo Agustín, José Ignacio, Marco Buzunáriz, Miguel ángel
Tipo de recurso: capítulo de libro
Fecha de publicación:2006
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/53268
Acceso en línea:https://hdl.handle.net/20.500.14352/53268
Access Level:acceso abierto
Palabra clave:514
Line arrangements
Alexander Invariant
Geometría
1204 Geometría
Descripción
Sumario:Following the general strategy proposed by G.Rybnikov, we present a proof of his well-known result, that is, the existence of two arrangements of lines having the same combinatorial type, but nonisomorphic fundamental groups. To do so, the Alexander Invariant and certain invariants of combinatorial line arrangements are presented and developed for combinatorics with only double and triple points. This is part of a more general project to better understand the relationship between topology and combinatorics of line arrangements.