Burak Ozbagci (Koc University, Istanbul)

Title: Nonorientable open books

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.