Nicholson, J;
(2021)
On CW-complexes over groups with periodic cohomology.
Transactions of the American Mathematical Society
, 374
pp. 6531-6557.
10.1090/tran/8411.
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Abstract
If G has 4-periodic cohomology, then finite D2 complexes over G are determined up to polarised homotopy by their Euler characteristic if and only if G has at most two one-dimensional quaternionic representations. We use this to solve Wall’s D2 problem for several infinite families of non-abelian groups and, in these cases, also show that any finite Poincar´e 3-complex X with G = π1(X) admits a cell structure with a single 3-cell. The proof involves cancellation theorems for ZG modules where G has periodic cohomology.
| Type: | Article |
|---|---|
| Title: | On CW-complexes over groups with periodic cohomology |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/tran/8411 |
| Publisher version: | http://dx.doi.org/10.1090/tran/8411 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10136686 |
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