Search results for "Low-Dimensional topology"

showing 2 items of 2 documents

Vassiliev invariants for braids on surfaces

2000

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the considered surface.

Surface (mathematics)Fundamental groupLow-dimensional topologyGeneral MathematicsBraid groupGroup Theory (math.GR)braidMathematics::Algebraic TopologyCombinatoricsMathematics - Geometric TopologyMathematics::Group TheoryMathematics::Category TheoryMathematics::Quantum Algebra20F36 (Primary) 57M2757N05 (Secondary)BraidFOS: MathematicssurfaceMathematicsApplied MathematicsGeometric Topology (math.GT)Mathematics::Geometric TopologyFinite type invariantVassiliev Invariantfinite type invariantIsomorphismMathematics - Group TheoryGroup theory
researchProduct

Equivalence relations among homology 3-spheres and the Johnson filtration

2021

The Torelli group of a surface consists of isotopy classes of homeomorphisms of this surface acting trivially at the homological level. The structure of the Torelli group can be approached by the study and the comparison of two filtrations of this group: its lower central series, and the "Johnson" filtration, given by the kernels of the natural actions on the successive nilpotent quotients of the fundamental group of the surface. It is now known that there are, via the notion of "Heegaard splittings", rich interactions between this 2-dimensional study and the study of some 3-manifolds topological invariants: we refer here precisely to the so-called "finite-type" invariants. In this PhD, we …

Topologie de petite dimensionTopological invariantsGroupe de TorelliTorelli groupLow-Dimensional topologyInvariants topologiques[MATH.MATH-GN] Mathematics [math]/General Topology [math.GN]
researchProduct