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For oriented connected closed manifolds of the same dimension, there is a transitive relation: $M$ dominates $N$, or $M ge N$, if there exists a continuous map of non-zero degree from $M$ onto $N$. Section 1 is a reminder on the notion of degree (Brouwer, Hopf), Section 2 shows examples of domination and a first set of obstructions to domination due to Hopf, and Section 3 describes obstructions in terms of Gromovs 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 notion for groups (fundamental groups), due to D. Kotschick and C. Loh: a group is presentable by a product if it contains two infinite commuting subgroups which generate a subgroup of finite index. The last section shows a small sample of groups which are not presentable by products; examples include appropriate Coxeter groups.
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and certain geomet
We give a different and possibly more accessible proof of a general Borsuk--Ulam theorem for a product of spheres, originally due to Ramos. That is, we show the non-existence of certain $(mathbb{Z}/2)^k$-equivariant maps from a product of $k$ spheres
The (non)triviality of Samelson products of the inclusions of the spheres into p-regular exceptional Lie groups is completely determined, where a connected Lie group is called p-regular if it has the p-local homotopy type of a product of spheres.
We study which quadratic forms are representable as the local degree of a map $f : A^n to A^n$ with an isolated zero at $0$, following the work of Kass and Wickelgren who established the connection to the quadratic form of Eisenbud, Khimshiashvili, a
The domination polynomials of binary graph operations, aside from union, join and corona, have not been widely studied. We compute and prove recurrence formulae and properties of the domination polynomials of families of graphs obtained by various pr