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Cambridge Journal of Mathematics
Volume 8 (2020)
Number 2
The index and nullity of the Lawson surfaces $\xi_{g,1}$
Pages: 363 – 405
DOI: https://dx.doi.org/10.4310/CJM.2020.v8.n2.a3
Authors
Abstract
We prove that the Lawson surface $\xi_{g,1}$ in Lawson’s original notation, which has genus $g$ and can be viewed as a desingularization of two orthogonal great two-spheres in the round three-sphere $\mathbb{S}^3$, has index $2g + 3$ and nullity $6$ for any genus $g \geq 2$. In particular $\xi_{g,1}$ has no exceptional Jacobi fields, which means that it cannot “flap its wings” at the linearized level and is $C^1$-isolated.
Nikolaos Kapouleas was partially supported by NSF grant DMS-1405537.
Received 23 May 2019
Published 21 April 2020