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, Volume 152, Issue 1–2, pp 1–60 | Cite as

Tropical Hopf manifolds and contracting germs

  • Matteo Ruggiero
  • Kristin ShawEmail author


Classical Hopf manifolds are compact complex manifolds whose universal covering is \(\mathbb {C}^d \backslash \{0\}\). We investigate the tropical analogues of Hopf manifolds, and relate their geometry to tropical contracting germs. To do this we develop a procedure called monomialization which transforms non-degenerate tropical germs into morphisms, up to tropical modification. A link is provided between tropical Hopf manifolds and the analytification of Hopf manifolds over a non-archimedean field. We conclude by computing the tropical Picard group and (pq)-homology groups.

Mathematics Subject Classification:

Primary 14T05 Secondary 37P50 


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.IMJUniversité Paris 7Paris Cedex 13France
  2. 2.Technische Universität BerlinBerlinGermany

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