Weiss derivatives of holomorphic maps

TL;DR

This paper introduces a new orthogonal approach to understanding the stable homotopy types of spaces of holomorphic maps to projective space, providing explicit computations and a new proof of a known stable splitting.

Contribution

It develops the Weiss towers for holomorphic and continuous maps, proving polynomiality for holomorphic maps and explicitly computing the continuous case, leading to new insights.

Findings

Weiss towers for holomorphic maps are polynomial.

Explicit computation of Weiss towers for continuous maps.

New proof of Cohen--Cohen--Mann--Milgram stable splitting.

Abstract

We propose an orthogonal approach to the stable homotopy type of spaces of holomorphic maps to projective space. We study the Weiss towers of the unitary functors of holomorphic and continuous maps to $\mathbb{P}(V)$, and show that the former is polynomial and completely compute the latter. As an application we give a new proof of a stable splitting of Cohen--Cohen--Mann--Milgram.