Abstract: Consider a once punctured surface bundle over the circle. Perron-Rolfsen shows that having an Alexander polynomial with real positive roots is a sufficient condition for the bundle to have bi-orderable fundamental group. This is done by showing the action of the monodromy induced on the fundamental group of the surface preserves a “standard” bi-ordering. In this talk, we discuss if there are other ways to bi-order the fundamental group of a punctured torus bundle. This work is joint with Henry Segerman.
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