Finite order q-invariants of immersions of surfaces into 3-space

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Given a surface F, we are interested in ℤ/2 valued invariants of immersions of F into ℝ3, which are constant on each connected component of the complement of the quadruple point discriminant in Imm(F, ℝ3). Such invariants will be called "g-invariants." Given a regular homotopy class A ⊆ Imm(F, ℝ3), we denote by Vn(A) the space of all q-invariants on A of order ≤ n. We show that if F is orientable, then for each regular homotopy class A and each n, dim( Vn(A)/Vn-1(A)) ≤ 1.

Original languageEnglish
Pages (from-to)215-221
Number of pages7
JournalMathematische Zeitschrift
Issue number2
StatePublished - Feb 2001


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