7 citations · 10 across the 9 of their papers we have counts for
10 papers
Enumerating corank 2 complex vector bundles on odd complex projective spaces
Yang Hu, Morgan Opie
For odd, we enumerate rank complex topological vector bundles on with prescribed complex -theory class. The answer exhibits a 24-fold periodicity and…
High-corank torsion in homotopy of unitary groups via topological modular forms and higher real -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…
On algebraic vector bundles of rank over smooth affine fourfolds
Thomas Brazelton, Morgan Opie, Tariq Syed
The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquel…
Enumerating stably trivial vector bundles with higher real -theory
Hood Chatham, Yang Hu, Morgan Opie
This paper explores periodic phenomena in the group of stably trivial, complex rank topological vector bundles on $\mathbb{CP}^{r+c…
Rank-preserving additions for topological vector bundles, after a construction of Horrocks
Morgan Opie
We produce group structures on certain sets of topological vector bundles of fixed rank. In particular, we put a group structure on complex rank bundles on with…
A classification of complex rank 3 vector bundles on complex projective 5-space
Morgan Opie
Given integers , there is a complex rank topological bundle on with -th Chern class equal to if and only if satisfy the Schwa…
Cofibration category of digraphs for path homology
Daniel Carranza, Brandon Doherty, Chris Kapulkin +3
We prove that the category of directed graphs and graph maps carries a cofibration category structure in which the weak equivalences are the graph maps inducing isomorphisms on pat…
The trace of the local -degree
Thomas Brazelton, Robert Burklund, Stephen McKean +2
We prove that the local -degree of a polynomial function at an isolated zero with finite separable residue field is given by the trace of the local -deg…
Localization in Homotopy Type Theory
J. Daniel Christensen, Morgan Opie, Egbert Rijke +1
We study localization at a prime in homotopy type theory, using self maps of the circle. Our main result is that for a pointed, simply connected type , the natural map $X \to X_…
Extremal divisors on moduli spaces of rational curves with marked points
Morgan Opie
We study effective divisors on , focusing on hypertree divisors introduced by Castravet and Tevelev and the proper transforms of divisors on $\overline{M}_{1,n-…