%0 Journal Article
%T Straight homotopy invariants
%A S. S. Podkorytov
%J Mathematics
%D 2014
%I arXiv
%X Let $X$ and $Y$ be spaces and $M$ be an abelian group. A homotopy invariant $f\colon [X,Y]\to M$ is called straight if there exists a homomorphism $F\colon L(X,Y)\to M$ such that $f([a])=F(\langle a\rangle)$ for all $a\in C(X,Y)$. Here $\langle a\rangle\colon\langle X\rangle\to\langle Y\rangle$ 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.
%U http://arxiv.org/abs/1405.0396v2