# REIDEMEISTER ORBIT SETS ON THE MAPPING TORUS

Lee, Seoung-Ho

• Published : 2004.10.01
• 36 3

#### Abstract

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Let f : G $\longrightarrow$ G be an endomorphism between the fundamental group of the mapping torus. Extending Jiang and Ferrario's works on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets of f relative to Reidemeister sets on suspension groups. In particular, if f is an automorphism, an similar formula for Reidemeister orbit sets of f relative to Reidemeister sets on given groups is also proved.

#### Keywords

Reidemeister sets;Reidemeister orbit sets;suspension groups

#### References

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