Realification of stably trivial vector bundles

Guy Boyde; Niall Taggart

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arXiv · 2606.26837

Realification of stably trivial vector bundles

Guy Boyde·Niall Taggart

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Abstract

The set of stably trivial complex vector bundles over complex projective spaces and spheres has a natural group structure when the corank is small enough. With respect to this group structure, the operations of taking the underlying real vector bundle (realification) and of adding a trivial line bundle (stabilisation), are group homomorphisms. Building on Hu's recent enumerations of stably trivial complex bundles, we compute these homomorphisms in a range by using Weiss calculus to translate the problem to stable homotopy theory.

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Guy Boyde, Niall Taggart. 2026-06-25. Realification of stably trivial vector bundles. https://arxiv.org/abs/2606.26837

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