TY - JOUR
T1 - An obstruction to embedding 2-dimensional complexes into the 3-sphere
AU - Eto, Kazufumi
AU - Matsuzaki, Shosaku
AU - Ozawa, Makoto
PY - 2016/2/1
Y1 - 2016/2/1
N2 - 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.
AB - 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.
KW - 3-Sphere
KW - CW complex
KW - Embedding
KW - Multibranched surface
KW - Obstruction
UR - http://www.scopus.com/inward/record.url?scp=84949008957&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84949008957&partnerID=8YFLogxK
U2 - 10.1016/j.topol.2015.11.008
DO - 10.1016/j.topol.2015.11.008
M3 - Article
AN - SCOPUS:84949008957
SN - 0166-8641
VL - 198
SP - 117
EP - 125
JO - Topology and its Applications
JF - Topology and its Applications
ER -