Metastable Complex Vector Bundles over Complex Projective Spaces
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Date
2024-01-09
Authors
Hu, Yang
Journal Title
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Publisher
University of Oregon
Abstract
In the unstable range, topological vector bundles over finite CW complexes are difficult to classify in general. Over complex projective spaces \mathbb{C}P^n, such bundles are far from being fully classified, or even enumerated, except for a few small dimensional cases studied in the 1970's using classical tools from homotopy theory, and more recently using the modern tool of chromatic homotopy theory. We apply another modern tool, Weiss calculus, to enumerate topological complex vector bundles over \mathbb{C}P^n with trivial Chern class data, in the first two cases of the metastable range.