Crosscap numbers of pretzel knots

Details Crosscap numbers of pretzel knots Crosscap numbers of pretzel knots

2006-08-21

arxiv.org/abs/math/0608480v2

Mathematics

Geometric Topology

13 pages, 10 figures, v2: An assumption of the main theorem is clarified

Scientific paper

The crosscap number of a knot in the 3-sphere is defined as the minimal first
Betti number of non-orientable subsurfaces bounded by the knot. In this paper,
we determine the crosscap numbers of pretzel knots. The key ingredient to
obtain the result is the algorithm of enumerating all essential surfaces for
Montesinos knots developed by Hatcher and Oertel.

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