Homology, Homotopy and Applications

Volume 22 (2020)

Number 1

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

Pages: 375 – 390

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n1.a21


Shizuo Kaji (Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan)

Shintarô Kuroki (Faculty of Science, Department of Applied Mathematics, Okayama University of Science, Okayama-shi, Okayama, Japan)

Eunjeong Lee (Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, South Korea)

Dong Youp Suh (Department of Mathematical Sciences, Korea Institute of Science and Technology (KAIST), Daejeon, South Korea)


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.


flag Bott towers of general Lie type, flag Bott manifold, generalized Bott manifold, flag manifold, equivariant cohomology

2010 Mathematics Subject Classification

Primary 14M15, 55R10. Secondary 57S25.

Kaji was partially supported by KAKENHI, Grant-in-Aid for Scientific Research (C) 18K03304. Kuroki was supported by JSPS KAKENHI Grant Number 17K14196. Lee was supported by IBS-R003-D1. Suh was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No. 2016R1A2B4010823).

Received 6 May 2019

Received revised 17 August 2019

Accepted 13 August 2019

Published 8 January 2020