Doodle groups

Khovanov, Mikhail

doi:10.1090/S0002-9947-97-01706-6

Doodle groups
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by Mikhail Khovanov PDF

Trans. Amer. Math. Soc. 349 (1997), 2297-2315 Request permission

Abstract:

A doodle is a finite number of closed curves without triple intersections on an oriented surface. There is a “fundamental” group, naturally associated with a doodle. In this paper we study these groups, in particular, we show that fundamental groups of some doodles are automatic and give examples of doodles whose fundamental groups have non-trivial center.

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