Surfaces in products of two curves

A. Koyama*, J. Krasinkiewicz, S. Spież

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)618-640
Number of pages23
JournalTopology and its Applications
Publication statusPublished - 2015 Dec


  • Cohomology groups
  • Embeddings
  • Surfaces
  • Symmetric products

ASJC Scopus subject areas

  • Geometry and Topology


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