Intrinsic Chirality of Graphs in 3-manifolds

The main result of this paper is that for every closed, connected, orientable, irreducible 3-manifold $M$, there is an integer $n_M$ such that any abstract graph with no automorphism of order 2 which has a 3-connected minor whose genus is more than $n_M$ has no achiral embedding in $M$. By contrast, the paper also proves that for every graph $γ$, there are infinitely many closed, connected, orientable, irreducible 3-manifolds $M$ such that some embedding of $γ$ in $M$ is pointwise fixed by an orientation reversing involution of $M$.

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