M. Crabb

collaborators

Showing math.ATShow all

3 papers · 1 filter

math.AT2025

Dold indices and symmetric powers

M. C. Crabb

Results of Macdonald and Dold from the 1960s and '70s expressing the Lefschetz numbers of symmetric powers of a self-map of a compact ENR in terms of the Lefschetz numbers of itera…

math.AT2025

A Poincaré-Hopf theorem for n-valued vector fields

M. C. Crabb

The Poincaré-Hopf theorem for line fields, as described in a paper of Crowley and Grant, is interpreted as a special case of a Poincaré-Hopf theorem for $n$ -valued sections of a ve…

math.AT2024

A Borsuk--Ulam theorem for well separated maps

M. C. Crabb

Suppose that $f_{1}, \dots, f_{m} : S (V) \to R$ are $m$ ( $\geq 1$ ) continuous functions defined on the unit sphere in a Euclidean vector space $V$ of dimension $m + 1$ satisfying $f_i(-v)…