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Dong Youp Suh

Publications and source records attributed to Dong Youp Suh.

23 records · Page 2Linked to original sources
arXiv2008

Topological classification of generalized Bott towers

If $B$ is a toric manifold and $E$ is a Whitney sum of complex line bundles over $B$, then the projectivization $P(E)$ of $E$ is again a toric manifold. Starting with $B$ as a point and repeating this construction, we obtain a sequence of complex projective bundles which we call a generalized Bott tower. We prove that if the top manifold in the tower has the same cohomology ring as a product of complex projective spaces, then every fibration in the tower is trivial so that the top manifold is diffeomorphic to the product of complex projective spaces. This gives a supporting evidence to what we call cohomological rigidity problem for toric manifolds "Are toric manifolds diffeomorphic (or homeomorphic) if their cohomology rings are isomorphic?" We provide two more results which support the cohomological rigidity problem.

math.AT↗
arXiv2003

On extensions of representations for compact Lie groups

Let $H$ be a closed normal subgroup of a compact Lie group $G$ such that $G/H$ is connected. This paper provides a necessary and sufficient condition for every complex representation of $H$ to be extendible to $G$, and also for every complex $G$-vector bundle over the homogeneous space $G/H$ to be trivial. In particular, we show that the condition holds when the fundamental group of $G/H$ is torsion free.

math.RT↗
arXiv2000

Classification of equivariant real vector bundles over a circle

This is a continuation of the authors' previous work [math.AT/9910001] on classification of equivariant complex vector bundles over a circle. In this paper we classify equivariant real vector bundles over a circle with a compact Lie group action, by characterizing the fiber representations of them, and by using the result of the complex case. We also treat the triviality of them. The basic phenomenon is similar to the complex case but more complicated here.

math.AT↗
arXiv1999

Classification of Equivariant Complex Vector Bundles over a Circle

In this paper we characterize the fiber representations of equivariant complex vector bundles over a circle and classify these bundles. We also treat the triviality of equivariant complex vector bundles over a circle by investigating the extensions of representations. As a corollary of our results, we calculate the reduced equivariant K-group of a circle for any compact Lie group.

math.AT↗