New York Journal of Mathematics
Volume 30 (2024), 502-512


Andrew Ronan

Completion preserves homotopy fibre squares of connected nilpotent spaces

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Published: March 31, 2024.
Keywords: nilpotent, spaces, groups, localisation, completion, homotopy, homotopy fibre square, homotopy pullback, T-complete, fracture theorem.
Subject [2010]: 55P60, 55R05, 20F18.

We prove that completion preserves homotopy fibre squares of connected nilpotent spaces. As an application, we deduce the Hasse fracture square associated to a connected nilpotent space. Along the way, we record some closure properties of the category of T-complete nilpotent groups, where T is a non-empty set of primes.


The author gratefully acknowledges funding from the University of Warwick and the UK Engineering and Physical Sciences Research Council (Grant number: EP/R513374/1).

Author information

Andrew Ronan
Zeeman Building
University of Warwick
Coventry, CV4 7EZ, UK