On the enumeration of Fano Bott manifolds

TL;DR

This paper establishes a bijective correspondence between Fano Bott manifolds and signed rooted forests, enabling enumeration of their classes and revealing connections to rooted triangular cacti.

Contribution

It introduces a novel bijective correspondence that allows enumeration of Fano Bott manifolds and links to combinatorial structures like rooted triangular cacti.

Findings

Enumerated isomorphism classes of Fano Bott manifolds

Enumerated diffeomorphism classes of indecomposable Fano Bott manifolds

Connected signed rooted forests to rooted triangular cacti

Abstract

Fano Bott manifolds bijectively correspond to signed rooted forests with some equivalence relation. Using this bijective correspondence, we enumerate the isomorphism classes of Fano Bott manifolds and the diffeomorphism classes of indecomposable Fano Bott manifolds. We also observe that the signed rooted forests with the equivalence relation bijectively correspond to rooted triangular cacti.