# 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01335377
Contributor : Carlos Simpson <>
Submitted on : Tuesday, June 21, 2016 - 9:27:51 PM
Last modification on : Tuesday, December 8, 2020 - 9:39:36 AM

### Identifiers

• HAL Id : hal-01335377, version 1
• ARXIV : 1503.00989

### Citation

Ludmil Katzarkov, Alexander Noll, Pandit Pranav, Carlos Simpson. Constructing Buildings and Harmonic Maps. 2016. ⟨hal-01335377⟩

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