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Constructing Buildings and Harmonic Maps

Part of the Progress in Mathematics book series (PM,volume 324)

Abstract

In a continuation of our previous work [21], we outline a theory which should lead to the construction of a universal pre-building and versal building with a φ-harmonic map from a Riemann surface, in the case of twodimensional buildings for the group SL3. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for SL2. Our conjectural construction would determine the exponents for SL3 WKB problems, and it can be put into practice on examples.

Mathematics Subject Classification (2010).

  • Primary: 14H30; Secondary: 34E20
  • 51E24
  • 30F15
  • 30F30

Keywords

  • Building
  • Grothendieck topology
  • polyhedral complex
  • spectral curve
  • spectral network
  • BPS state
  • WKB exponent

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  • DOI: 10.1007/978-3-319-59939-7_6
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Correspondence to Ludmil Katzarkov .

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Katzarkov, L., Noll, A., Pandit, P., Simpson, C. (2017). Constructing Buildings and Harmonic Maps. In: Auroux, D., Katzarkov, L., Pantev, T., Soibelman, Y., Tschinkel, Y. (eds) Algebra, Geometry, and Physics in the 21st Century. Progress in Mathematics, vol 324. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59939-7_6

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