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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05774 |
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| _version_ | 1866914115580067840 |
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| author | Li, Kevin Loeh, Clara Moraschini, Marco Sauer, Roman Uschold, Matthias |
| author_facet | Li, Kevin Loeh, Clara Moraschini, Marco Sauer, Roman Uschold, Matthias |
| contents | We present an axiomatic approach to combination theorems for various homological properties of groups and, more generally, of chain complexes. Examples of such properties include algebraic finiteness properties, $\ell^2$-invisibility, $\ell^2$-acyclicity, lower bounds for Novikov--Shubin invariants, and vanishing of homology growth. As a key example, we introduce an algebraic version of Abért--Bergeron--Frączyk--Gaboriau's cheap rebuilding property that implies vanishing of torsion homology growth and fits into our axiomatic framework for combination theorems. In particular, we obtain that certain graphs of groups with amenable vertex groups and elementary amenable edge groups have vanishing torsion homology growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The algebraic cheap rebuilding property Li, Kevin Loeh, Clara Moraschini, Marco Sauer, Roman Uschold, Matthias Group Theory Algebraic Topology 20J06, 20E26 We present an axiomatic approach to combination theorems for various homological properties of groups and, more generally, of chain complexes. Examples of such properties include algebraic finiteness properties, $\ell^2$-invisibility, $\ell^2$-acyclicity, lower bounds for Novikov--Shubin invariants, and vanishing of homology growth. As a key example, we introduce an algebraic version of Abért--Bergeron--Frączyk--Gaboriau's cheap rebuilding property that implies vanishing of torsion homology growth and fits into our axiomatic framework for combination theorems. In particular, we obtain that certain graphs of groups with amenable vertex groups and elementary amenable edge groups have vanishing torsion homology growth. |
| title | The algebraic cheap rebuilding property |
| topic | Group Theory Algebraic Topology 20J06, 20E26 |
| url | https://arxiv.org/abs/2409.05774 |