### Jiang-type theorems for coincidences of maps into homogeneous spaces

DOI: http://dx.doi.org/10.12775/TMNA.2008.008

#### Abstract

Let $f,g\colon X\to G/K$ be maps from a closed connected orientable

manifold $X$ to an orientable coset space $M=G/K$ where $G$ is

a compact connected Lie group, $K$ a closed subgroup and $\dim X=\dim M$.

In this paper, we show that if $L(f,g)=0$ then $N(f,g)=0$; if $L(f,g)\ne 0$

then $N(f,g)=R(f,g)$ where $L(f,g), N(f,g)$, and $R(f,g)$ denote the Lefschetz,

Nielsen, and Reidemeister coincidence numbers of $f$ and $g$, respectively.

When $\dim X> \dim M$, we give conditions under which $N(f,g)=0$ implies $f$

and $g$ are deformable to be coincidence free.

manifold $X$ to an orientable coset space $M=G/K$ where $G$ is

a compact connected Lie group, $K$ a closed subgroup and $\dim X=\dim M$.

In this paper, we show that if $L(f,g)=0$ then $N(f,g)=0$; if $L(f,g)\ne 0$

then $N(f,g)=R(f,g)$ where $L(f,g), N(f,g)$, and $R(f,g)$ denote the Lefschetz,

Nielsen, and Reidemeister coincidence numbers of $f$ and $g$, respectively.

When $\dim X> \dim M$, we give conditions under which $N(f,g)=0$ implies $f$

and $g$ are deformable to be coincidence free.

#### Keywords

Lefschetz coincidence number; Nielsen coincidence number; Reidemeister coincidence number; Jiang-type theorems; homogeneous spaces

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