## African Diaspora Journal of Mathematics

### Rational Pairing Rank of a Map

Toshihiro Yamaguchi

#### Abstract

We define a rational homotopy invariant, the rational pairing rank $v_0(f)$ of a map $f:X\to Y$, which is a natural generalization of the rational pairing rank $v_0(X)$ of a space $X$ [16]. It is upper-bounded by the rational LS-category $cat_0(f)$ and lower-bounded by an invariant $g_0(f)$ related to the rank of Gottlieb group. Also it has a good estimate for a fibration $X\overset{j}{\to} E\overset{p}{\to} Y$ such as $v_0(E)\leq v_0(j) +v_0(p)\leq v_0(X) +v_0(Y)$.

#### Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 19, Number 1 (2016), 1-11.

Dates
First available in Project Euclid: 9 June 2016