The Graded Cobordism Group of Codimension-One Immersions |
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Authors: | L Funar R Gini |
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Institution: | (1) Institut Fourier BP 74, UMR 5582 CNRS, University of Grenoble I, 38402 Saint-Martin-dHères cedex, France;(2) Department of Mathematics, University of Pisa, via Buonarroti 2, 56127 Pisa, Italy |
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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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