Surfaces in products of two curves

A. Koyama, J. Krasinkiewicz, S. Spież

Research output: Contribution to journalArticlepeer-review

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
Pages (from-to)618-640
Number of pages23
JournalTopology and its Applications
Volume196
DOIs
Publication statusPublished - 2015 Dec

Keywords

  • Cohomology groups
  • Embeddings
  • Surfaces
  • Symmetric products

ASJC Scopus subject areas

  • Geometry and Topology

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