Guy Boyde

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20202026

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math.AT2026

Realification of stably trivial vector bundles

Guy Boyde, Niall Taggart

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 grou…

math.AT2025

The dga of planar loops when $2 n = 4$

Guy Boyde

The dga of planar loops is a pictorial chain complex introduced in a recent paper of the author, Boyd, Randal-Williams, and Sroka, where a minimal model for it was given. In the fi…

math.AT2021

$Z / p^{r}$ -hyperbolicity via homology

Guy Boyde

We show that the homotopy groups of a Moore space $P^{n} (p^{r})$ , where $p^{r} \neq = 2$ , are $Z / p^{s}$ -hyperbolic for $s \leq r$ . Combined with work of Huang-Wu, Neisendorfer, and…

math.AT2020

Bounding size of homotopy groups of spheres

Guy Boyde

Let $p$ be prime. We prove that, for $n$ odd, the $p$ -torsion part of $π_{q} (S^{n})$ has cardinality at most $p^{2^{\frac{1}{p - 1} (q - n + 3 - 2 p)}}$ , and hence has rank at most $2^{\frac{1…

Realification of stably trivial vector bundles

The dga of planar loops when 2n=4

Z/pr-hyperbolicity via homology

Bounding size of homotopy groups of spheres

The dga of planar loops when $2 n = 4$

$Z / p^{r}$ -hyperbolicity via homology