The graded cobordism group of codimension-one immersions

2001/04/30 by Louis Funar, Rosa Gini
Mathematics · #math.GT #msc:57 #msc:50 #msc:10

paper · pdf

published as G.A.F.A. 12(2002), 1235-1264. · revised version, G.A.F.A. (to appear), 23p., 3 figures

arxiv created 2002/09/24 · arxiv updated 2009/11/30

Abstract

The cobordism group N(Mⁿ) of codimension-one immersions in the n-manifold Mⁿ has a natural filtration induced by any cellular decomposition. The problem addressed in this paper is the explicit computation of the graded group gr^*N(Mⁿ). We introduce some new invariants for immersions enlightening the Atiyah-Hirzebruch spectral sequence associated to N(M), which are of combinatorial-geometric nature. Explicit computations are developed for n≤7, and the group structure is also investigated for orientable 4-manifolds.

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