Year: 2014
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Podkorytov, S. S.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2275815482