A Singularity Theorem for Twistor Spinors

Belgun, Florin Alexandru; Ginoux, Nicolas; Rademacher, Hans-Bert

Annales de l'Institut Fourier, Tome 57 (2007) no. 4, pp. 1135-1159.

Nous étudions les structures spin sur les orbifolds. Nous montrons en particulier que, si la codimension de l’ensemble des singularités est supérieure à 2, alors une orbifold est spin si et seulement si sa partie lisse l’est. Nous prouvons également que, sur une orbifold compacte, tout spineur-twisteur non identiquement nul admet au plus un zéro qui est alors singulier sauf si l’orbifold est conformément équivalente à une sphère ronde. Nous illustrons l’optimalité de nos résultats sur des exemples.

We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.

Classification : 53C21, 53A30, 32C10
Keywords: Orbifolds, twistor-spinors, ALE spaces
Mot clés : orbifolds, spineurs-twisteurs, espaces ALE

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