𝑆1-fibred nil Bott surfaces and the fundamental groups / 𝑆1-fibred nil Bott 曲面とその基本群
- Resource Type
- Journal Article
- Authors
- Mayumi Nakayama; 中山 雅友美
- Source
- 長岡工業高等専門学校研究紀要 / Research Reports of National Institute of Technology, Nagaoka College. 2021, 57:21
- Subject
- Klein Bottle
fundamental group
𝑆1 bundle
- Language
- Japanese
- ISSN
- 0027-7568
2432-3241
Torus and Klein Bottle are compact quotient manifolds R2/Γ by an action of a torsionfree discrete properly discontinuous normal subgroup Γof R2⋊O(2) on the Euclidean plane R2. It is well known that a fundamental group of a compact quotient manifold R2/Γ is isomorphic to Γ. In this paper, I verify that the fundamental group of Klein Bottle has a faithful representation to R2⋊ O(2) in terms of an 𝑆1-fibred nil Bott manifold.