Obiettivo The complexity of a 3-manifold is a certain integer that rigorously expresses an intuitive estimation of how complicated the manifold is. Being a rather natural and powerful invariant (for instance, only finitely many closed irreducible manifolds can share a given complexity), it plays an important role in dealing with one of the central problems of low-dimensional topology, namely the classification of 3-manifolds. However, its exact position with respect to the rest of 3-dimensional topology, and particularly its connections with other 3-manifold invariants, are not fully understood yet. Only relations with homology and the hyperbolic volume have been explicitly described so far.The aim of the project is to fill this gap (at least to some extent), by establishing connections of complexity with invariants other than homology and the volume, and by exploring several new approaches to complexity. In particular, we expect to discover relations with the theory of quantum invariants, which play an especially important role in the above-mentioned classification task. To meet this goal, we plan to found a certain new combinatorial technique for treating framed links in 3-manifolds. Since surgery on framed links has a crucial importance within the theory of quantum invariants, we believe that this technique will also be a helpful tool for studying these invariants for their own sake.Furthermore, we would like to develop the theory of complexity in several other directions, specifically to analyse its connection with domination between 3-manifolds and to investigate certain notions of complexity for 3-orbifolds and knots. Meeting these aims will use, among other tools, methods relevant to other branches of mathematics, such as geometric group theory and the theory o f accessibility in groups. The foundation of these methods that is foreseen in the course of the project can be expected to make a useful contribution to these areas as well. Campo scientifico medical and health sciencesclinical medicinesurgerynatural sciencesmathematicspure mathematicstopologyalgebraic topology Parole chiave 3-manifolds 3-orbifolds algorithmic topology branched spines complexity of 3-manifolds framed links knots quantum invariants of 3-manifolds special spines Programma(i) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Argomento(i) MOBILITY-2.3 - Marie Curie Incoming International Fellowships (IIF) Invito a presentare proposte FP6-2005-MOBILITY-7 Vedi altri progetti per questo bando Meccanismo di finanziamento IIF - Marie Curie actions-Incoming International Fellowships Coordinatore UNIVERSITÀ DI PISA Contributo UE Nessun dato Indirizzo Lungarno Pacinotti 43/44 PISA Italia Mostra sulla mappa Collegamenti Sito web Opens in new window Costo totale Nessun dato
