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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. |
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Abstract
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.
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| Acknowledgements
The author gratefully acknowledges funding from the University of Warwick and the UK Engineering and Physical Sciences Research Council (Grant number: EP/R513374/1).
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| Author information
Andrew Ronan
Zeeman Building
University of Warwick
Coventry, CV4 7EZ, UK
Andrew.Ronan@Warwick.ac.uk
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