Homology, Homotopy and Applications

Volume 25 (2023)

Number 1

Coformality around fibrations and cofibrations

Pages: 235 – 248


Ruizhi Huang (Institute of Mathematics, Academy of Mathematics and Systems Sciences, C.A.S., Beijing, China)


We show that in a fibration the coformality of the base space implies the coformality of the total space under reasonable conditions, and these conditions can not be weakened. The result is partially dual to the classical work of Lupton on the formality within a fibration. Our result has two applications. Firstly, we show that for certain homotopy cofibrations, the coformality of the cofiber implies the coformality of the middle space. Secondly, we show that the total spaces of certain spherical fibrations are Koszul.


coformal space, Sullivan model, fibration, cofibration, Koszul space, rational LS category

2010 Mathematics Subject Classification


Copyright © 2023, Ruizhi Huang. Permission to copy for private use granted.

Ruizhi Huang was supported in part by NSFC (Grant nos. 11801544 and 12288201), the National Key R&D Program of China (No. 2021YFA1002300), the Youth Innovation Promotion Association of CAS, and the “Chen Jingrun” Future Star Program of AMSS.

Received 13 January 2022

Received revised 6 May 2022

Accepted 6 May 2022

Published 12 April 2023