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For oriented connected closed manifolds of the same dimension, there is atransitive relation: $M$ dominates $N$, or $M \ge N$, if there exists acontinuous map of non-zero degree from $M$ onto $N$. Section 1 is a reminder onthe notion of degree (Brouwer, Hopf), Section 2 shows examples of dominationand a first set of obstructions to domination due to Hopf, and Section 3describes obstructions in terms of Gromov's simplicial volume.  In Section 4 we address the particular question of when a given manifold can(or cannot) be dominated by a product. These considerations suggest a notionfor groups (fundamental groups), due to D. Kotschick and C. L\"oh: a group ispresentable by a product if it contains two infinite commuting subgroups whichgenerate a subgroup of finite index. The last section shows a small sample ofgroups which are not presentable by products; examples include appropriateCoxeter groups.

Brouwer degree, domination of manifolds, and groups presentable by products