Skip to main content
Go to the home page of the European Commission (opens in new window)
English en
CORDIS - EU research results
CORDIS
Content archived on 2024-05-29

Use of combinatorial methods in various approaches to three-dimensional topology

Objective

Since the work of Poi care, topologists have been looking for a comprehensive classification of three-dimensional manifolds and links. Recently, this quest has enjoyed spectacular developments based on various approaches to three-dimensional topology, namely contact topology, hyperbolic geometry and quantum topology with its cousin, the theory of finite-type invariants. Only little is known about the relationship between these independent theories. Nevertheless, according to work of Bernadette and Petrolia, each of these theories can be a tackled using standard spine of three-dimensional manifolds. Standard spines provide combinatorial methods to present three-dimensional manifolds as well as the additional structures with which they can be equipped. This methodology has already proved to be fruitful. Therefore, one could expect the theory of standard spines to become the node of some connections between hyperbolic geometry; contact topology and quantum topology in dimension three. The proposed project looks towards this perspective and, in the shorter term, addresses two problems pointing in that direction. The first of these problems consists in investigating connections between the theory of standard spines and the recent theory of finite-type invariants of compact oriented three-dimensional manifolds, which is due to Goussarov and Habra. A similar problem stands for refinements of these theories to manifolds equipped with Spin-structures or Eller structures. The second subject is that of Reidemeister-Turaev torsion of three-dimensional manifolds endowed with Eller structures. One interesting question is to compute the multiplicative variation of the torsion invariant under appropriate surgery modifications of the manifold. These computations, which have been started in Massuyeau? S thesis could be completed thanks to some extensions of this invariant due to Bernadette and Petrolia. Again, their techniques involve the use of standard spines.

Fields of science (EuroSciVoc)

CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.

You need to log in or register to use this function

Keywords

Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)

Topic(s)

Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.

Call for proposal

Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.

FP6-2002-MOBILITY-5
See other projects for this call

Funding Scheme

Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.

EIF - Marie Curie actions-Intra-European Fellowships

Coordinator

UNIVERSITA DEGLI STUDI DI PISA
EU contribution
No data
Address
Via Lungarno Pacinotti 43
PISA
Italy

See on map

Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

No data
My booklet 0 0