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

Kazufumi Eto, Shosaku Matsuzaki, Makoto Ozawa

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)117-125
    Number of pages9
    JournalTopology and its Applications
    Volume198
    DOIs
    Publication statusPublished - 2016 Feb 1

    Fingerprint

    CW-complex
    Obstruction
    Dual Graph
    System of Linear Equations
    Integral Solution
    Homology Groups
    Complement

    Keywords

    • 3-Sphere
    • CW complex
    • Embedding
    • Multibranched surface
    • Obstruction

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

    An obstruction to embedding 2-dimensional complexes into the 3-sphere. / Eto, Kazufumi; Matsuzaki, Shosaku; Ozawa, Makoto.

    In: Topology and its Applications, Vol. 198, 01.02.2016, p. 117-125.

    Research output: Contribution to journalArticle

    Eto, Kazufumi ; Matsuzaki, Shosaku ; Ozawa, Makoto. / An obstruction to embedding 2-dimensional complexes into the 3-sphere. In: Topology and its Applications. 2016 ; Vol. 198. pp. 117-125.
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