G. Arone

activity

20052024

most citedOn the rational homology of high dimensional analogues of spaces of long knots

33 citations · 115 across the 24 of their papers we have counts for

collaborators

Showing math.ATShow all

24 papers · 1 filter

math.AT2024★ 2 cited

The spectrum of excisive functors

Gregory Arone, Tobias Barthel, Drew Heard +1

We prove a thick subcategory theorem for the category of $d$ -excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=…

math.AT2023

Intrinsic convergence of the homological Taylor tower for $r$ -immersions in $R^{n}$

Gregory Arone, Franjo Sarcevic

For an integer $r \geq 2$ , the space of $r$ -immersions of $M$ in $R^{n}$ is defined to be the space of immersions of $M$ in $R^{n}$ such that at most $r - 1$ points of $M$ are mapped to…

math.AT2022

The space of $r$ -immersions of a union of discs in $R^{n}$

Gregory Arone, Franjo Sarcevic

For a manifold $M$ and an integer $r > 1$ , the space of $r$ -immersions of $M$ in $R^{n}$ is defined to be the space of immersions of $M$ in $R^{n}$ such that the preimage…

math.AT2021

Suspension spectra of matrix algebras, the rank filtration, and rational noncommutative CW-spectra

Gregory Arone, Ilan Barnea, Tomer M. Schlank

In a companion paper [ABS1] we introduced the stable $\infty$ -category of noncommutative CW-spectra, which we denoted $NSp$ . Let $M$ denote the full spectrally e…

math.AT2021

Noncommutative CW-spectra as enriched presheaves on matrix algebras

Gregory Arone, Ilan Barnea, Tomer M. Schlank

Motivated by the philosophy that $C^{*}$ -algebras reflect noncommutative topology, we investigate the stable homotopy theory of the (opposite) category of $C^{*}$ -algebras. We focus on…

math.AT2021

Embedding obstructions in $R^{d}$ from the Goodwillie-Weiss calculus and Whitney disks

Gregory Arone, Vyacheslav Krushkal

Given a finite CW complex $K$ , we use a version of the Goodwillie-Weiss tower to formulate an obstruction theory for embedding $K$ into a Euclidean space $R^{d}$ . For $2$ -di…

The spectrum of excisive functors

Intrinsic convergence of the homological Taylor tower for r-immersions in Rn

The space of r-immersions of a union of discs in Rn

Suspension spectra of matrix algebras, the rank filtration, and rational noncommutative CW-spectra

Noncommutative CW-spectra as enriched presheaves on matrix algebras

Embedding obstructions in Rd from the Goodwillie-Weiss calculus and Whitney disks

Intrinsic convergence of the homological Taylor tower for $r$ -immersions in $R^{n}$

The space of $r$ -immersions of a union of discs in $R^{n}$

Embedding obstructions in $R^{d}$ from the Goodwillie-Weiss calculus and Whitney disks