Some \ZZ₃ⁿ-equivariant triangulations of \CPⁿ

2014/05/11 by Soumen Sarkar, Sarkar, Soumen
Mathematics · #05E18 #57Q15 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1405.2568

openalex publication_date 2014/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1983, Banchoff and Kuhnel constructed a minimal triangulation of \CP² with 9 vertices. \CP³ was first triangulated by Bagchi and Datta in 2012 with 18 vertices. Known lower bound on number of vertices of a triangulation of \CPⁿ is 1 + ((n + 1)²)/(2) for n ≥ 3. We give explicit construction of some triangulations of complex projective space \CPⁿ with \frac4ⁿ⁺¹-13 vertices for all n. No explicit triangulation of \CPⁿ is known for n ≥ 4.

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