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

^*この研究の対応する著者

基幹理工学部

研究成果: Article › 査読

抄録

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”.

本文言語	English
ページ（範囲）	618-640
ページ数	23
ジャーナル	Topology and its Applications
巻	196
DOI	https://doi.org/10.1016/j.topol.2015.05.037
出版ステータス	Published - 2015 12月

ASJC Scopus subject areas

幾何学とトポロジー

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10.1016/j.topol.2015.05.037

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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",

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

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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

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U2 - 10.1016/j.topol.2015.05.037

DO - 10.1016/j.topol.2015.05.037

M3 - Article

AN - SCOPUS:84930260594

VL - 196

SP - 618

EP - 640

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

ER -

Surfaces in products of two curves

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