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RESEARCH PRODUCT

Topological invariants of stable immersions of oriented 3-manifolds in R4

C. CasonattoR. Wik AtiqueM. C. Romero Fuster

subject

Discrete mathematicsConnected componentPure mathematicsFirst order local Vassiliev type invariantsFirst ordersymbols.namesakeEuler characteristicsymbolsTopological invariantsGeometry and TopologyInvariant (mathematics)Stable immersionsSINGULARIDADESMathematics

description

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.

yearjournalcountryeditionlanguage
2012-02-01Topology and its Applications
10.1016/j.topol.2011.09.016http://dx.doi.org/10.1016/j.topol.2011.09.016