Polynomial Charts for Totally Unordered Languages

Proceedings of the 16th Nordic Conference of Computational Linguistics NODALIDA-2007. Editors: Joakim Nivre, Heiki-Jaan Kaalep, Kadri Muischnek and Mare Koit. University of Tartu, Tartu, 2007. ISBN 978-9985-4-0513-0 (online) ISBN 978-9985-4-0514-7 (CD-ROM) pp. 183-190

Contents

Proceedings of the 16th Nordic Conference of Computational Linguistics NODALIDA-2007. Editors: Joakim Nivre, Heiki-Jaan Kaalep, Kadri Muischnek and Mare Koit. University of Tartu, Tartu, 2007. ISBN 978-9985-4-0513-0 (online) ISBN 978-9985-4-0514-7 (CD-ROM) pp. iii-viii

Conference Program

Proceedings of the 16th Nordic Conference of Computational Linguistics NODALIDA-2007. Editors: Joakim Nivre, Heiki-Jaan Kaalep, Kadri Muischnek and Mare Koit. University of Tartu, Tartu, 2007. ISBN 978-9985-4-0513-0 (online) ISBN 978-9985-4-0514-7 (CD-ROM) pp. xiii-xviii

The complexity of the classification of Riemann surfaces and complex manifolds

In answer to a question by Becker, Rubel, and Henson, we show that countable subsets of ℂ can be used as complete invariants for Riemann surfaces considered up to conformal equivalence, and that this equivalence relation is itself Borel in a natural Borel structure on the space of all such surfaces. We further proceed to precisely calculate the classification difficulty of this equivalence relation in terms of the modern theory of Borel equivalence relations. On the other hand we show that the analog of Becker, Rubel, and Henson's question has a negative solution in (complex) dimension n ≥ 2