# Flag Bott manifolds of general Lie type and their equivariant cohomology rings

## TL;DR

This paper introduces a new class of geometric objects called flag Bott manifolds of general Lie type, generalizing previous notions, and computes their equivariant cohomology rings, advancing understanding of their topological and algebraic structure.

## Contribution

The paper defines flag Bott manifolds of general Lie type and provides explicit calculations of their torus equivariant cohomology rings, extending known results to a broader class.

## Key findings

- Explicit formulas for equivariant cohomology rings
- Generalization of flag Bott and Bott manifolds
- New insights into torus actions on these manifolds

## Abstract

In this article we introduce flag Bott manifolds of general Lie type as the total spaces of iterated flag bundles. They generalize the notion of flag Bott manifolds and generalized Bott manifolds, and admit nice torus actions. We calculate the torus equivariant cohomology rings of flag Bott manifolds of general Lie type.