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: http://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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