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Bulletin of the London Mathematical Society (1)

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THE NIELSEN KERNEL OF AN ARBITRARY RIEMANN SURFACE
MATTHEW M. JONES
Journal:

Bulletin of the London Mathematical Society / Volume 38 / Issue 5 / October 2006

Published online by Cambridge University Press:

20 September 2006, pp. 825-828

Print publication:

October 2006
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By considering coverings of surfaces by annuli, we extend previous results concerning the Nielsen kernel of topologically finite Riemann surfaces to arbitrary orbifolds. Specifically, we show that the length of a boundary loop in the Nielsen kernel is strictly greater than twice the length of the corresponding boundary loop of its orbifold, and that the infinite Nielsen kernel has empty interior.