Morgan Opie

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20242026

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math.AT2026

Enumerating corank 2 complex vector bundles on odd complex projective spaces

Yang Hu, Morgan Opie

For $n$ odd, we enumerate rank $n$ complex topological vector bundles on $C P^{n + 2}$ with prescribed complex $K$ -theory class. The answer exhibits a 24-fold periodicity and…

math.AT2026

High-corank torsion in homotopy of unitary groups via topological modular forms and higher real $K$ -theories

Hood Chatham, Yang Hu, Morgan Opie

Work of Toda identifies groups of metastable vector bundles on even-dimensional spheres with stable homotopy groups of certain stunted projective spectra. Using Weiss' unitary calc…

math.AT2024

A classification of complex rank 3 vector bundles on complex projective 5-space

Morgan Opie

Given integers $a_{1}, a_{2}, a_{3}$ , there is a complex rank $3$ topological bundle on $C P^{5}$ with $i$ -th Chern class equal to $a_{i}$ if and only if $a_{1}, a_{2}, a_{3}$ satisfy the Schwa…

Enumerating corank 2 complex vector bundles on odd complex projective spaces

High-corank torsion in homotopy of unitary groups via topological modular forms and higher real K-theories

A classification of complex rank 3 vector bundles on complex projective 5-space

High-corank torsion in homotopy of unitary groups via topological modular forms and higher real $K$ -theories