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

2015/03/07 by Kazufumi Eto, Eto, Kazufumi, Shosaku Matsuzaki +3
Mathematics · #57N35 (Secondary) #57Q35 (Primary) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.CO #math.GT #msc:57N35 #msc:57Q35

paper · pdf · doi:10.48550/arxiv.1503.02170

10 page, 11 figures

arxiv created 2015/03/29 · arxiv updated 2015/03/31

Abstract

We consider an embedding of a 2-dimensional CW complex into the 3-sphere, and construct it's 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.

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