M. C. Crabb

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20102022

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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)…

math.AT2022

Topology of the Grünbaum--Hadwiger--Ramos problem for mass assignments

Pavle V. M. Blagojević, Jaime Calles Loperena, Michael C. Crabb +1

In this paper, motivated by recent work of Schnider and Axelrod-Freed \& Soberón, we study an extension of the classical Grünbaum--Hadwiger--Ramos mass partition problem to mass as…

math.AT2015

$Z_{2}$ -bordism and the Borsuk-Ulam Theorem

Michael C. Crabb, Daciberg L. Goncalves, Alice K. M. Libardi +1

The purpose of this work is to classify, for given integers $m, n \geq 1$ , the bordism class of a closed smooth $m$ -manifold $X$ with a free smooth involution $τ$ with respect to…

math.AT2010

The geometric Hopf invariant and double points

Michael Crabb, Andrew Ranicki

The geometric Hopf invariant of a stable map F is a stable Z_2-equivariant map h(F) such that the stable Z_2-equivariant homotopy class of h(F) is the primary obstruction to F bein…

A Borsuk--Ulam theorem for well separated maps

Topology of the Grünbaum--Hadwiger--Ramos problem for mass assignments

Z2​-bordism and the Borsuk-Ulam Theorem

The geometric Hopf invariant and double points

$Z_{2}$ -bordism and the Borsuk-Ulam Theorem