A subexponential size triangulation of $\mathbb{R}P^n$

TL;DR

This paper presents a groundbreaking construction of a triangulation of real projective space with subexponential size, significantly improving upon previous exponential bounds in combinatorial topology.

Contribution

It introduces a novel method to construct triangulations of al{RP}^n with subexponential size, breaking the longstanding exponential barrier.

Findings

Triangulation size of al{RP}^n is e^{(rac{1}{2}+o(1))\u221a{n}\u221a{\u03bb{n}}}

Achieved the first subexponential triangulation of al{RP}^n

Breaks exponential size barrier in combinatorial topology

Abstract

We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a trianglation of $\mathbb{RP}^n$ of size $e^{(\frac{1}{2}+o(1))\sqrt{n}{\log n}}$.