Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-20T02:52:07.474Z Has data issue: false hasContentIssue false
  • English
  • Français

Classification of Bott Manifolds up to Dimension 8

Published online by Cambridge University Press:  10 December 2014

Suyoung Choi
Suyoung Choi*
Affiliation:
Department of Mathematics, Ajou University, San 5, Woncheondong, Yeongtonggu, Suwon 443-749, Republic of Korea (schoi@ajou.ac.kr)
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that three- and four-stage Bott manifolds are classified up to diffeomorphism by their integral cohomology rings. In addition, any cohomology ring isomorphism between two three-stage Bott manifolds can be realized by a diffeomorphism between the Bott manifolds.

Keywords

Bott towerBott manifoldcohomological rigiditystrong cohomological rigidityPrimary 57S25Secondary 22F30
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 3 , October 2015 , pp. 653 - 659
Copyright
Copyright © Edinburgh Mathematical Society 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces I, Am. J. Math. 80 (1958), 458–538.Google Scholar
2.Choi, S. and Masuda, M., Classification of ℚ-trivial Bott manifolds, J. Symplectic Geom. 10(3) (2012), 447–462.CrossRefGoogle Scholar
3.Choi, S., Masuda, M. and Suh, D. Y., Topological classification of generalized Bott towers, Trans. Am. Math. Soc. 362(2) (2010), 1097–1112.Google Scholar
4.Choi, S., Masuda, M. and Suh, D. Y., Rigidity problems in toric topology: a survey, Proc. Steklov Inst. Math. 275 (2011), 177–190.Google Scholar
5.Hirzebruch, F., Über eine Klasse von einfachzusammenhäangenden komplexen Mannigfaltigkeiten, Math. Annalen 124 (1951), 77–86.Google Scholar
6.Ishida, H., (Filtered) cohomological rigidity of Bott towers, Osaka J. Math. 49(2 (2012), 515–522.Google Scholar
7.Masuda, M. and Panov, T. E., Semi-free circle actions, Bott towers, and quasitoric manifolds, Mat. Sb. 199(8 (2008), 95–122.Google Scholar