Description
Abstract:
After reviewing some basic results about nonorientable open books in dimension three, we will show that the monodromy of Klassen’s nonorientable genus two open book on $P^2 \times S^1$ is the Y-homeomorphism of Lickorish (a.k.a. the crosscap slide)---which is a primary example of a surface homeomorphism that cannot be factorized into Dehn twists. We will also show that the nonorientable $S^2$-bundle over $S^1$ admits a genus two open book with connected binding, whose monodromy is the crosscap transposition---another example of a surface homeomorphism that cannot be factorized into Dehn twists. Moreover, we will discuss a few simple observations about nonorientable open books, which are well-known for “orientable” open books in dimension three.
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