Two transformations of simple polytopes preserving moment-angle manifolds

TL;DR

This paper introduces two new operations on simple polytopes, biflip and puzzle-move, which produce different polytopes with the same moment-angle manifolds, advancing understanding of their topological invariance.

Contribution

The paper presents novel polytope transformations that preserve the diffeomorphism type of associated moment-angle manifolds, expanding the toolkit for studying their topological properties.

Findings

Biflip operation preserves moment-angle manifold diffeomorphism class.

Puzzle-move operation also preserves the diffeomorphism class.

These transformations provide new ways to generate polytopes with equivalent topological properties.

Abstract

We introduce two operations named biflip and puzzle-move on simple polytopes producing polytopes with diffeomorphic moment-angle manifolds.