Brittenham, Mark; Hermiller, Susan Tame filling invariants for groups. (English) Zbl 1364.20024 Int. J. Algebra Comput. 25, No. 5, 813-854 (2015). Summary: A new pair of asymptotic invariants for finitely presented groups, called intrinsic and extrinsic tame filling functions, is introduced. These filling functions are quasi-isometry invariants that strengthen the notions of intrinsic and extrinsic diameter functions for finitely presented groups. We show that the existence of a (finite-valued) tame filling functions implies that the group is tame combable. Bounds on both intrinsic and extrinsic tame filling functions are discussed for stackable groups, including groups with a finite complete rewriting system, Thompson’s group \(F\), and almost convex groups. Cited in 4 Documents MSC: 20F65 Geometric group theory 20F06 Cancellation theory of groups; application of van Kampen diagrams 20F69 Asymptotic properties of groups Keywords:filling invariant; rewriting system; almost convex group; stackable group PDFBibTeX XMLCite \textit{M. Brittenham} and \textit{S. Hermiller}, Int. J. Algebra Comput. 25, No. 5, 813--854 (2015; Zbl 1364.20024) Full Text: DOI arXiv References: [1] DOI: 10.1090/conm/372/06880 · doi:10.1090/conm/372/06880 [2] M. Bridson, Invitations to Geometry and Topology, Oxford Graduate Texts in Mathematics 7 (Oxford University Press, Oxford, 2002) pp. 29–91. [3] Bridson M., J. Differential Geom. 82 pp 115– (2009) · Zbl 1165.49040 · doi:10.4310/jdg/1242134370 [4] DOI: 10.1007/BF00181266 · Zbl 0607.20020 · doi:10.1007/BF00181266 [5] DOI: 10.1007/s00209-010-0759-5 · Zbl 1256.20040 · doi:10.1007/s00209-010-0759-5 [6] DOI: 10.1016/S0021-8693(03)00516-7 · Zbl 1054.20022 · doi:10.1016/S0021-8693(03)00516-7 [7] DOI: 10.1007/978-1-4613-9730-4_9 · doi:10.1007/978-1-4613-9730-4_9 [8] DOI: 10.1017/CBO9780511661860.008 · doi:10.1017/CBO9780511661860.008 [9] DOI: 10.1007/s00222-005-0462-z · Zbl 1166.20024 · doi:10.1007/s00222-005-0462-z [10] DOI: 10.1090/S0002-9947-00-02717-3 · Zbl 0988.20026 · doi:10.1090/S0002-9947-00-02717-3 [11] Lyndon R. C., Classics in Mathematics, in: Combinatorial Group Theory (2001) · doi:10.1007/978-3-642-61896-3 [12] DOI: 10.1090/S0002-9947-97-01772-8 · Zbl 0883.57003 · doi:10.1090/S0002-9947-97-01772-8 [13] Thiel C., Bonner Mathematische Schriften, in: Zur Fast-Konvexität Einiger Nilpotenter Gruppen (1992) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.