An obstruction to embedding 2-dimensional complexes into the 3-sphere

We consider an embedding of a 2-dimensional CW complex into the 3-sphere, and construct its dual graph. Then we obtain a homogeneous system of linear equations from the 2-dimensional CW complex in the first homology group of the complement of the dual graph. By checking that the homogeneous system o...

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Bibliographic Details
Published in:Topology and its applications 2016-02, Vol.198, p.117-125
Main Authors: Eto, Kazufumi, Matsuzaki, Shosaku, Ozawa, Makoto
Format: Article
Language:English
Subjects:
3-Sphere
CW complex
Embedding
Multibranched surface
Obstruction
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Summary:We consider an embedding of a 2-dimensional CW complex into the 3-sphere, and construct its dual graph. Then we obtain a homogeneous system of linear equations from the 2-dimensional CW complex in the first homology group of the complement of the dual graph. By checking that the homogeneous system of linear equations does not have an integral solution, we show that some 2-dimensional CW complexes cannot be embedded into the 3-sphere.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2015.11.008