Homology, Homotopy and Applications

Volume 12 (2010)

Number 1

On the Wu invariants for immersions of a graph into the plane

Pages: 45 – 60

DOI: https://dx.doi.org/10.4310/HHA.2010.v12.n1.a5

Author

Ryo Nikkuni (Department of Mathematics, Tokyo Woman’s Christian University, Tokyo, Japan)

Abstract

We give an explicit calculation of the Wu invariants for immersions of a finite graph into the plane and classify all generic immersions of a graph into the plane up to regular homotopy by the Wu invariant. This result is a generalization of the fact that two plane curves are regularly homotopic if and only if they have the same rotation number.

Keywords

immersion, graph, Wu invariant

2010 Mathematics Subject Classification

57M15, 57Q35

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Published 1 January 2010