Surfaces in products of two curves

Akira Koyama, J. Krasinkiewicz, S. Spiez

    Research output: Contribution to journalArticle

    Abstract

    We present a detailed discussion of the problem of embeddability of connected closed surfaces into products of two curves. In particular, we comment on two important results by R. Cauty and W. Kuperberg in this direction and strengthen them. It is proved that a closed connected surface M lying in a product of two curves is a retract of the product if and only if M is a torus. It is also observed the fact that every compact connected bordered surface embeds in the "three-page-book".

    Original languageEnglish
    JournalTopology and its Applications
    DOIs
    Publication statusAccepted/In press - 2014 Jan 30

    Fingerprint

    Curve
    Closed
    Embeddability
    Retract
    Torus
    If and only if

    Keywords

    • Cohomology groups
    • Embeddings
    • Primary
    • Secondary
    • Surfaces
    • Symmetric products

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

    Surfaces in products of two curves. / Koyama, Akira; Krasinkiewicz, J.; Spiez, S.

    In: Topology and its Applications, 30.01.2014.

    Research output: Contribution to journalArticle

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    KW - Symmetric products

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