5 papers
New perspectives on a classical embedding theorem
M. C. Crabb
In this expository note, recent results of Kishimoto and Matsushita on triangulated manifolds are linked to the classical criterion on the normal Stiefel-Whitney classes for existe…
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…
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 -valued sections of a ve…
A hyperplane Ham Sandwich theorem
M. C. Crabb
We give a direct proof of a result due to Karasev (2008), Karasev-Matschke (2014) and Schnider-Soberón (2023). Given Borel probability measures on the space of affine hyperpl…
A Borsuk--Ulam theorem for well separated maps
M. C. Crabb
Suppose that are () continuous functions defined on the unit sphere in a Euclidean vector space of dimension satisfying $f_i(-v)…