Topological invariants of stable immersions of oriented 3-manifolds in

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• 作者：C. Casonatto^a ; ¹ ; ^{ccasonatto@famat.ufu.br} ; M.C. Romero Fuster^b ; ² ; ^{Carmen.Romero@uv.es} ; R. Wik Atique^c ; ³ ; ^{rwik@icmc.usp.br}
• 关键词：57R45 ; 58K15 ; 58K65
• 刊名：Topology and its Applications
• 出版年：2012
• 出版时间：1 February 2012
• 年：2012
• 卷：159
• 期：2
• 页码：420-429
• 全文大小：281 K

文摘

We show that the -module of first order local Vassiliev type invariants of stable immersions of oriented 3-manifolds into is generated by 3 topological invariants: The number of pairs of quadruple points and the positive and negative linking invariants and introduced by V. Goryunov (1997) . 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.