Guy Boyde

activity

20202026

most citedSome asymptotic formulae for torsion in homotopy groups

2 citations · 3 across the 5 of their papers we have counts for

collaborators

8 papers

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.AT2024

The Goodwillie calculus of polyhedral products

Guy Boyde, Niall Taggart

We describe the Goodwillie calculus of polyhedral products in the case that the fat wedge filtration on the associated real moment-angle complex is trivial. We do this by analysing…

math.AT2023★ 2 cited

Some asymptotic formulae for torsion in homotopy groups

Guy Boyde, Ruizhi Huang

Inspired by a remarkable work of Félix, Halperin and Thomas on the asymptotic estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors on lo…

math.AT2022

Growth of homotopy groups of spheres via the Goodwillie-EHP Sequence

Guy Boyde

We bound the volume of the homotopy groups of the 2-local Goodwillie approximations of a sphere in terms of the amount of $2$ -torsion in the stable stems, providing a Goodwillie-th…

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.AT2021

$p$ -hyperbolicity of homotopy groups via $K$ -theory

Guy Boyde

We show that $S^{n} \lor S^{m}$ is $Z / p^{r}$ -hyperbolic for all primes $p$ and all $r \in Z^{+}$ , provided $n, m \geq 2$ , and consequently that various spaces containing $…

math.AT2020★ 1 cited

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

The Goodwillie calculus of polyhedral products

Some asymptotic formulae for torsion in homotopy groups

Growth of homotopy groups of spheres via the Goodwillie-EHP Sequence

Z/pr-hyperbolicity via homology

p-hyperbolicity of homotopy groups via K-theory

Bounding size of homotopy groups of spheres

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

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

$p$ -hyperbolicity of homotopy groups via $K$ -theory