On the topological complexity of toral relatively hyperbolic groups

Li, Kevin

doi:10.1090/proc/15733

On the topological complexity of toral relatively hyperbolic groups
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Proc. Amer. Math. Soc. 150 (2022), 967-974 Request permission

Abstract:

We prove that the topological complexity $\operatorname {TC}(\pi )$ equals $cd(\pi \times \pi )$ for certain toral relatively hyperbolic groups $\pi$.

References

Zbigniew Błaszczyk, José Gabriel Carrasquel-Vera, and Arturo Espinosa Baro, On the sectional category of subgroup inclusions and Adamson cohomology theory, J. Pure Appl. Algebra 226 (2022), no. 6, Paper No. 106959, 18. MR 4343838, DOI 10.1016/j.jpaa.2021.106959
Pietro Capovilla, Clara Löh, and Marco Moraschini. Amenable category and complexity. Preprint, arXiv:2012.00612, 2020, Algebr. Geom. Topol., to appear.
Alexander Dranishnikov, On topological complexity of hyperbolic groups, Proc. Amer. Math. Soc. 148 (2020), no. 10, 4547–4556. MR 4135318, DOI 10.1090/proc/15094
Alexander Dranishnikov, On dimension of product of groups, Algebra Discrete Math. 28 (2019), no. 2, 203–212. MR 4072474
Michael Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003), no. 2, 211–221. MR 1957228, DOI 10.1007/s00454-002-0760-9
Michael Farber, Mark Grant, Gregory Lupton, and John Oprea, Bredon cohomology and robot motion planning, Algebr. Geom. Topol. 19 (2019), no. 4, 2023–2059. MR 3995023, DOI 10.2140/agt.2019.19.2023
Michael Farber and Stephan Mescher, On the topological complexity of aspherical spaces, J. Topol. Anal. 12 (2020), no. 2, 293–319. MR 4119108, DOI 10.1142/S1793525319500511
Martin Fluch. On Bredon (co-)homological dimension of groups. PhD thesis, arXiv:1009.4633, 2010.
Wolfgang Lück, Survey on classifying spaces for families of subgroups, Infinite groups: geometric, combinatorial and dynamical aspects, Progr. Math., vol. 248, Birkhäuser, Basel, 2005, pp. 269–322. MR 2195456, DOI 10.1007/3-7643-7447-0_{7}
Wolfgang Lück and Michael Weiermann, On the classifying space of the family of virtually cyclic subgroups, Pure Appl. Math. Q. 8 (2012), no. 2, 497–555. MR 2900176, DOI 10.4310/PAMQ.2012.v8.n2.a6
Denis V. Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc. 179 (2006), no. 843, vi+100. MR 2182268, DOI 10.1090/memo/0843