On The Applications of Stiefel-Whitney Classes of Real Bott Manifolds

Daniel Danladi¹ , Domven Lohcwat² , Isah Abdullahi³

1. Dept. of Mathematics, Karl Kumm University, Vom Plateau State.
2. Dept. of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria.
3. Dept. of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria.

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.4 , pp.34-37, Aug-2024

Online published on Aug 31, 2024

Copyright © Daniel Danladi, Domven Lohcwat, Isah Abdullahi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

64 Views    63 Downloads    25 Downloads

Abstract :
Real Bott manifolds are a type of compact, connected Riemannian manifolds without boundaries, notable as a unique and intriguing category of real toric varieties. This study focuses on identifying a set of topological invariants known as Stiefel-Whitney classes, which are crucial characteristic classes in the context of the set of integers modulo two. We computed the Stiefel-Whitney classes of real Bott manifolds. We applied the method to calculate the Stiefel-Whitney classes of the manifolds. The formula for determining the number of terms in each class was also given.

Key-Words / Index Term :
Manifolds, Real Bott manifolds, Stiffel-Whiteney Class

References :
[1] L. S. Charlap, Bieberbach Groups and Flat Manifolds. Springer-Verlag, 1986.
[2] A. Szczepa?ski, Geometry of Crystallographic Groups. World Scientific, Algebra and Discrete Mathematics, vol. 4, 2012.
[3] R. Lee and R. Szczarba, "On the integral Pontrjagin classes of a Riemannian flat manifold," Geometriae Dedicata, vol. 3, no. 1, pp. 1-9, 1974.
[4] Y. Kamishima and M. Masuda, "Cohomological rigidity of real Bott manifolds," Algebraic & Geometric Topology, vol. 9, pp. 2479-2502, 2009.
[5] A. Gasior, "Note about Stiefel-Whitney classes on Real Bott Manifolds," arXiv preprint arXiv:1808.0803v1, 2018
[6] A. Gasior, "Note about Stiefel-Whitney classes on Real Bott Manifolds," arXiv:1808.0803v1 [math.GT], 2018.
[7] H. B. Lawson and M.-L. Michelsohn, Spin Geometry (PMS-38), Volume 38, vol. 84, Princeton, NJ: Princeton University Press, 2016.
[8] S. Choi, M. Masuda, and S.-i. Oum, "Classification of real bott manifolds and acyclic digraphs," Trans. Amer. Math. Soc., vol. 369, no. 4, pp. 2987-3011, 2016.
[9] S. Choi and S.-i. Oum, "Real bott manifolds and acyclic digraphs," arXiv preprint, arXiv:1002.4704, 2010.
[10] M.Grossberg and Y. Karshon, "Bott towers, complete integrability, and the extended character of representations," 1994.