A note on unliftable immersed surfaces in 3-space

Tsukasa Yashiro

doi:10.17654/gt019010019

A note on unliftable immersed surfaces in 3-space

Tsukasa Yashiro^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

An immersed surface in 3-space is a surface with double curves and isolated triple points. In general, immersed surfaces in 3-space are not images of embedded surface in 4-space under the orthogonal projection. In this paper, we present a sufficient condition about a triple point for an immersed surface to become an unliftable surface into 4-space. Also we construct an orientable unliftable immersed sphere.

Original language	English
Pages (from-to)	19-25
Number of pages	7
Journal	JP Journal of Geometry and Topology
Volume	19
Issue number	1
DOIs	https://doi.org/10.17654/gt019010019
Publication status	Published - Feb 2016

Keywords

Immersion
Liftable immersion
Surface

ASJC Scopus subject areas

Geometry and Topology

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10.17654/gt019010019

Cite this

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title = "A note on unliftable immersed surfaces in 3-space",

abstract = "An immersed surface in 3-space is a surface with double curves and isolated triple points. In general, immersed surfaces in 3-space are not images of embedded surface in 4-space under the orthogonal projection. In this paper, we present a sufficient condition about a triple point for an immersed surface to become an unliftable surface into 4-space. Also we construct an orientable unliftable immersed sphere.",

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author = "Tsukasa Yashiro",

note = "Publisher Copyright: {\textcopyright} 2016 Pushpa Publishing House, Allahabad, India.",

year = "2016",

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AB - An immersed surface in 3-space is a surface with double curves and isolated triple points. In general, immersed surfaces in 3-space are not images of embedded surface in 4-space under the orthogonal projection. In this paper, we present a sufficient condition about a triple point for an immersed surface to become an unliftable surface into 4-space. Also we construct an orientable unliftable immersed sphere.

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KW - Liftable immersion

KW - Surface

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A note on unliftable immersed surfaces in 3-space

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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