본문 바로가기
KERD
논문KCI 등재

EQUIVARIANT VECTOR BUNDLES OVER GRAPHS

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

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 \cite{CKMS}.

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 \cite{CKMS}.

참고문헌 (9)

  1. M. F. Atiyah, "K-Theory" (1989), Addison-Wesley
  2. T. Brocker, "Representations of compact Lie groups" (1985), Springer-Verlag
  3. J.-H. Cho, "Classification of equivariant complex vector bundles over a circle", J. Math. Kyoto Univ, 41(3), pp.517~534 (2001)
  4. 조진환, "Extending representations of $H$ to $G$ with discrete $G", H$, 2006, pp.43(1), 29~43[DOI]
  5. T. tom Dieck, "Transformation Groups" (1987), De Gruyter
  6. K. Kawakubo, "The Theory of Transformation Groups" (1991), Oxford University Press
  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, pp.414~420 (1959)

관련 논문AI추천

이 간행물의 다른 논문 (17건)