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Geodesic paths and weakly Mal'tsev categories

We introduce an algebraic structure with the purpose of modelling an arbitrary space with a suitable notion of geodesic path for every two points in it. We prove that this structure satisfies a weak Mal'tsev property, and show that any smooth surface in which every two points are linked by a unique geodesic path, in the sense of differential geometry, is an example of these kind of structures. The main application is intended to be in the theory of computation where a space with geodesics can now be considered as a simple algebraic structure satisfying some carefully chosen axioms. Joint work with J. P. Fatelo.

Date:  2014-03-18
Start Time:   15:30
Speaker:  Nelson Martins Ferreira (CDRSP, ESTG, IP Leiria)
Institution:  CDRSP, ESTG, Instituto Politécnico de Leiria
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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