Straight homotopy invariants

Abstract

Let $X$ and $Y$ be spaces and $M$ be an abelian group. A homotopy invariant $f:[X,Y]\to M$ is called straight if there exists a homomorphism $F:L(X,Y)\to M$ such that $f([a])=F(⟨a⟩)$ for all $a\in C(X,Y)$. Here $⟨a⟩:⟨X⟩\to ⟨Y⟩$ is the homomorphism induced by $a$ between the abelian groups freely generated by $X$ and $Y$ and $L(X,Y)$ is a certain group of `admissible' homomorphisms. We show that all straight invariants can be expressed through a `universal' straight invariant of homological nature.

Minor changes

References in corpus (2)

• An iterated sum formula for a spheroid's homotopy class modulo 2-torsion
• On homotopy invariants of finite degree

Cited by in corpus (1)

• Parametrized symmetric groups and the second homology of a group