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An n-dimensional Klein bottle

Part of: Differential topology Classical Topics in Algebraic Topology Homotopy theory

Published online by Cambridge University Press:  16 January 2019

Donald M. Davis
Donald M. Davis*
Affiliation:
Department of Mathematics, Lehigh University Bethlehem, PA 18015, USA (dmd1@lehigh.edu)
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Abstract

An n-dimensional analogue of the Klein bottle arose in our study of topological complexity of planar polygon spaces. We determine its integral cohomology algebra and stable homotopy type, and give an explicit immersion and embedding in Euclidean space.

Keywords

Klein bottleimmersionstopological complexitystable homotopy type

MSC classification

Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
Secondary: 55P15: Classification of homotopy type 57R42: Immersions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 5 , October 2019 , pp. 1207 - 1221
Copyright
Copyright © Royal Society of Edinburgh 2019 

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