0000000000294347
AUTHOR
R. Wik Atique
New techniques for classification of multigerms
Abstract The goal of these notes is to give an overview of the state of the art in classification of multigerms. We have tried to make them self-contained but certainly not extensive. The results included here scope most of the research on classification of multigerms carried out in the last 15 years with special emphasis on recent results by the authors of these notes and their collaborators.
Topological invariants of stable immersions of oriented 3-manifolds in R4
Abstract We show that the Z -module of first order local Vassiliev type invariants of stable immersions of oriented 3-manifolds into R 4 is generated by 3 topological invariants: The number of pairs of quadruple points and the positive and negative linking invariants l + and l − introduced by V. Goryunov (1997) [7] . We obtain the expression for the Euler characteristic of the immersed 3-manifold in terms of these invariants. We also prove that the total number of connected components of the triple points curve is a non-local Vassiliev type invariant.