The graded cobordism group of codimension-one immersions

Details The graded cobordism group of codimension-one immersions The graded cobordism group of codimension-one immersions

2001-04-03

arxiv.org/abs/math/0104037v2

G.A.F.A. 12(2002), 1235-1264.

Mathematics

Geometric Topology

revised version, G.A.F.A. (to appear), 23p., 3 figures

Scientific paper

The cobordism group $N(M^n)$ of codimension-one immersions in the $n$-manifold $M^n$ has a natural filtration induced by any cellular decomposition. The problem addressed in this paper is the explicit computation of the graded group $gr^*N(M^n)$. 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 $n\leq7$, and the group structure is also investigated for orientable 4-manifolds.

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