## African Diaspora Journal of Mathematics

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

### Rational Pairing Rank of a Map

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.adjm/1465472747

**Mathematical Reviews number (MathSciNet)**

MR3499093

**Zentralblatt MATH identifier**

1359.55009

**Subjects**

Primary: 55P62: Rational homotopy theory 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space 55R05: Fiber spaces 55Q70: Homotopy groups of special types [See also 55N05, 55N07]

**Keywords**

Gottlieb group LS-category of a map pairing rank of a map Gottlieb rank of a map Sullivan model rational homotopy Halperin conjecture

#### Citation

Yamaguchi, Toshihiro. Rational Pairing Rank of a Map. Afr. Diaspora J. Math. (N.S.) 19 (2016), no. 1, 1--11. https://projecteuclid.org/euclid.adjm/1465472747