Surfaces in products of two curves

A. Koyama; J. Krasinkiewicz; S. Spież

doi:10.1016/j.topol.2015.05.037

Surfaces in products of two curves

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

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	618-640
Number of pages	23
Journal	Topology and its Applications
Volume	196
DOIs	https://doi.org/10.1016/j.topol.2015.05.037
Publication status	Published - 2015 Dec

Keywords

Cohomology groups
Embeddings
Surfaces
Symmetric products

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2015.05.037

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@article{4125474c8eab481db45aca73982970dd,

title = "Surfaces in products of two curves",

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”.",

keywords = "Cohomology groups, Embeddings, Surfaces, Symmetric products",

author = "A. Koyama and J. Krasinkiewicz and S. Spie{\.z}",

note = "Funding Information: This work was supported by JSPS Grant-in-Aid for Scientific Research (C) Number 24540099 . Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

year = "2015",

month = dec,

doi = "10.1016/j.topol.2015.05.037",

language = "English",

volume = "196",

pages = "618--640",

journal = "Topology and its Applications",

issn = "0166-8641",

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TY - JOUR

T1 - Surfaces in products of two curves

AU - Koyama, A.

AU - Krasinkiewicz, J.

AU - Spież, S.

PY - 2015/12

Y1 - 2015/12

N2 - 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”.

AB - 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”.

KW - Cohomology groups

KW - Embeddings

KW - Surfaces

KW - Symmetric products

UR - http://www.scopus.com/inward/record.url?scp=84930260594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84930260594&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2015.05.037

DO - 10.1016/j.topol.2015.05.037

M3 - Article

AN - SCOPUS:84930260594

SN - 0166-8641

VL - 196

SP - 618

EP - 640

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Surfaces in products of two curves

Abstract

Keywords

ASJC Scopus subject areas

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