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Reduced 1-cohomology and relative property (T) |
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| Authors: | Talia Fernós Alain Valette Florian Martin |
| Institution: | 1. Einstein Institute of Mathematics, Hebrew University, 91904, Jerusalem, Israel 2. Institut de Mathématiques, Université de Neuchatel, Rue Emile Argand 11, 2007, Neuchatel, Switzerland 3. R&D Department, Philip Morris International, 2000, Neuchatel, Switzerland |
| Abstract: | Shalom characterized property (T) in terms of the vanishing of all reduced first cohomology for compactly generated groups. We characterize group pairs having the property that the restriction map on all first reduced cohomology vanishes. We show that, in a strong sense, this is inequivalent to relative property (T), even for compactly generated group-pairs. |
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