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Equilateral Convex Triangulations of ℝ P 2 $$\mathbb R P^2$$ with Three Conical Points of Equal Defect

In: In the Tradition of Thurston II

Author

Listed:
  • Mikhail Chernavskikh

    (Lomonosov Moscow State University)

  • Altan Erdnigor

    (HSE University, Russian Federation, Department of Mathematics)

  • Nikita Kalinin

    (Saint Petersburg State University)

  • Alexandr Zakharov

    (Saint Petersburg State University)

Abstract

Consider triangulations of ℝ P 2 $$\mathbb R P^2$$ whose all vertices have valency six except three vertices of valency 4. In this chapter we prove that the number f(n) of such triangulations with no more than n triangles grows as C ⋅ n2 + O(n3∕2) where , where is the Lobachevsky function and ζ ( Eis , 2 ) = ∑ ( a , b ) ∈ ℤ 2 ∖ 0 1 | a + b ω 2 | 4 $$\zeta (\mathit {Eis},2) =\sum \limits _{(a,b)\in \mathbb Z^2\setminus 0}{\frac {1}{|a+b\omega ^2|{ }^4}}$$ , and ω6 = 1.

Suggested Citation

  • Mikhail Chernavskikh & Altan Erdnigor & Nikita Kalinin & Alexandr Zakharov, 2022. "Equilateral Convex Triangulations of ℝ P 2 $$\mathbb R P^2$$ with Three Conical Points of Equal Defect," Springer Books, in: Ken’ichi Ohshika & Athanase Papadopoulos (ed.), In the Tradition of Thurston II, chapter 0, pages 315-329, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-97560-9_9
    DOI: 10.1007/978-3-030-97560-9_9
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