Article
| Title: | Flows of linear orders on sparse graphs (English) |
| Author: | Sullivan, Rob |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 66 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 87-102 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | We consider the topological dynamics of the automorphism group of a particular sparse graph $M_1$ resulting from an ab initio Hrushovski construction. We show that minimal subflows of the flow of linear orders on $M_1$ have all orbits meagre, partially answering a question of T. Tsankov regarding results of D. M. Evans, J. Hubička and J. Nešetřil on the topological dynamics of automorphism groups of sparse graphs. (English) |
| Keyword: | sparse graph |
| Keyword: | Hrushovski construction |
| Keyword: | admissible order |
| Keyword: | meagre orbit |
| Keyword: | orientation |
| MSC: | 03C15 |
| MSC: | 05C55 |
| MSC: | 05D10 |
| MSC: | 20B27 |
| MSC: | 37B05 |
| DOI: | 10.14712/1213-7243.2025.014 |
| . | |
| Date available: | 2026-05-15T05:57:43Z |
| Last updated: | 2026-05-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153611 |
| . | |
| Reference: | [1] Angel O., Kechris A. S., Lyons R.: Random orderings and unique ergodicity of automorphism groups.J. Eur. Math. Soc. (JEMS) 16 (2014), no. 10, 2059–2095. 10.4171/jems/483 |
| Reference: | [2] Ben Yaacov I., Melleray J., Tsankov T.: Metrizable universal minimal flows of Polish groups have a comeagre orbit.Geom. Funct. Anal. 27 (2017), no. 1, 67–77. 10.1007/s00039-017-0398-7 |
| Reference: | [3] Evans D. M.: Ample dividing.J. Symbolic Logic 68 (2003), no. 4, 1385–1402. 10.2178/jsl/1067620194 |
| Reference: | [4] Evans D. M.: Trivial stable structures with non-trivial reducts.J. London Math. Soc. (2) 72 (2005), no. 2, 351–363. 10.1112/S0024610705006435 |
| Reference: | [5] Evans D. M., Hubička J., Nešetřil J.: Automorphism groups and Ramsey properties of sparse graphs.available at arXiv:1801.01165v3 [math.GR] (2018), 49 pages. |
| Reference: | [6] Evans D. M., Hubička J., Nešetřil J.: Automorphism groups and Ramsey properties of sparse graphs.Proc. Lond. Math. Soc. (3) 119 (2019), no. 2, 515–546. 10.1112/plms.12238 |
| Reference: | [7] Evans D. M., Hubička J., Nešetřil J.: Ramsey properties and extending partial automorphisms for classes of finite structures.Fund. Math. 253 (2021), no. 2, 121–153. 10.4064/fm560-8-2020 |
| Reference: | [8] Hrushovski E.: A new strongly minimal set.Ann. Pure Appl. Logic 62 (1993), no. 2, 147–166. Zbl 0804.03020, 10.1016/0168-0072(93)90171-9 |
| Reference: | [9] Ivanov A. A.: Generic expansions of $\omega$-categorical structures and semantics of generalized quantifiers.J. Symbolic Logic 64 (1999), no. 2, 775–789. 10.2307/2586500 |
| Reference: | [10] Kechris A. S., Pestov V. G., Todorcevic S.: Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups.Geom. Funct. Anal. 15 (2005), no. 1, 106–189. 10.1007/s00039-005-0503-1 |
| Reference: | [11] Kechris A. S., Rosendal C.: Turbulence, amalgamation, and generic automorphisms of homogeneous structures.Proc. Lond. Math. Soc. (3) 94 (2007), no. 2, 302–350. 10.1112/plms/pdl007 |
| Reference: | [12] Nash-Williams C. St. J. A.: Decomposition of finite graphs into forests.J. London Math. Soc. 39 (1964), 12. |
| Reference: | [13] Nguyen Van Thé L.: More on the Kechris–Pestov–Todorcevic correspondence: precompact expansions.Fund. Math. 222 (2013), no. 1, 19–47. |
| Reference: | [14] Sullivan R.: Aspects of the Topological Dynamics of Sparse Graph Automorphism Groups.Ph.D. Thesis, Imperial College London, London, 2022. |
| Reference: | [15] Zucker A.: Topological dynamics of automorphism groups, ultrafilter combinatorics, and the generic point problem.Trans. Amer. Math. Soc. 368 (2016), no. 9, 6715–6740. 10.1090/tran6685 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
