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http://dx.doi.org/10.4134/JKMS.j150713

EQUIVARIANT VECTOR BUNDLES OVER GRAPHS  

Kim, Min Kyu (Department of Mathematics Education Gyeongin National University of Education)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 227-248 More about this Journal
Abstract
In this paper, we reduce the classification problem of equivariant (topological complex) vector bundles over a simple graph to the classification problem of their isotropy representations at vertices and midpoints of edges. Then, we solve the reduced problem in the case when the simple graph is homeomorphic to a circle. So, the paper could be considered as a generalization of [3].
Keywords
equivariant vector bundle; representation;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 M. F. Atiyah, K-Theory, Addison-Wesley, 1989.
2 T. Brocker and T. tom Dieck, Representations of compact Lie groups, Graduate Texts in Mathematics, vol. 98, Springer-Verlag, New York, 1985.
3 J.-H. Cho, S. S. Kim, M. Masuda, and D. Y. Suh, Classification of equivariant complex vector bundles over a circle, J. Math. Kyoto Univ. 41 (2001), no. 3, 517-534.   DOI
4 J.-H. Cho, M. Masuda, and D. Y. Suh, Extending representations of H to G with discrete G/H, J. Korean Math. Soc. 43 (2006), no. 1, 29-43.   DOI
5 T. tom Dieck, Transformation Groups, De Gruyter Studies in Mathematics, vol. 8, De Gruyter, Berlin-New York, 1987.
6 K. Kawakubo, The Theory of Transformation Groups, Oxford University Press, 1991.
7 M. K. Kim, Classification of equivariant vector bundles over two-sphere, arXiv:1005.0681.
8 M. K. Kim, Equivariant pointwise clutching maps, arXiv:1504.00159.
9 F. P. Peterson, Some remarks on Chern classes, Ann. of Math. (2) 69 (1959), 414-420.   DOI