Non-orientable fundamental surfaces in lens spaces

Details Non-orientable fundamental surfaces in lens spaces Non-orientable fundamental surfaces in lens spaces

2008-09-10

arxiv.org/abs/0809.1700v1

Mathematics

Geometric Topology

19 pages, 14 figures

Scientific paper

We give a concrete example of an infinite sequence of $(p_n, q_n)$-lens spaces $L(p_n, q_n)$ with natural triangulations $T(p_n, q_n)$ with $p_n$ taterahedra such that $L(p_n, q_n)$ contains a certain non-orientable closed surface which is fundamental with respect to $T(p_n, q_n)$ and of minimal crosscap number among all closed non-orientable surfaces in $L(p_n, q_n)$ and has $n-2$ parallel sheets of normal disks of a quadrilateral type disjoint from the pair of core circles of $L(p_n, q_n)$. Actually, we can set $p_0=0, q_0=1, p_{k+1}=3p_k+2q_k$ and $q_{k+1}=p_k+q_k$.

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