Constructing Buildings and Harmonic Maps

Abstract : In a continuation of our previous work, we outline a theory which should lead to the construction of a universal pre-building and versal building with a $\phi$-harmonic map from a Riemann surface, in the case of two-dimensional buildings for the group $SL_3$. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for $SL_2$. Our conjectural construction would determine the exponents for $SL_3$ WKB problems, and it can be put into practice on examples.
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Conference papers
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https://hal.univ-cotedazur.fr/hal-01331629
Contributor : Jean-Louis Thomin <>
Submitted on : Tuesday, June 14, 2016 - 11:03:00 AM
Last modification on : Thursday, May 3, 2018 - 1:32:58 PM

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  • HAL Id : hal-01331629, version 1
  • ARXIV : 1503.00989

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Ludmil Katzarkov, Alexander Noll, Pranav Pandit, Carlos Simpson. Constructing Buildings and Harmonic Maps. Algèbre, Géométrie et Physique : une conférence en l'honneur de Maxim Kontsevitch , Jun 2014, Paris, France. ⟨hal-01331629⟩

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