{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:38:06Z","timestamp":1759365486444,"version":"build-2065373602"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T00:00:00Z","timestamp":1728864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T00:00:00Z","timestamp":1728864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V048821\/1","EP\/V009044\/1","EP\/Y004302\/1"],"award-info":[{"award-number":["EP\/V048821\/1","EP\/V009044\/1","EP\/Y004302\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2025,10]]},"abstract":"Abstract<\/jats:title>\n Mohar recently adapted the classical game of Cops and Robber from graphs to metric spaces, thereby unifying previously studied pursuit-evasion games. He conjectured that finitely many cops can win on any compact geodesic metric space, and that their number can be upper-bounded in terms of the ranks of the homology groups when the space is a simplicial pseudo-manifold. We disprove these conjectures by constructing a metric on \n \n $$\\mathbb {S}^3$$<\/jats:tex-math>\n \n \n \n S<\/mml:mi>\n <\/mml:mrow>\n 3<\/mml:mn>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> with infinite cop number. More problems are raised than settled.<\/jats:p>","DOI":"10.1007\/s00454-024-00696-0","type":"journal-article","created":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T10:02:52Z","timestamp":1728900172000},"page":"793-804","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Compact Metric Spaces with Infinite Cop Number"],"prefix":"10.1007","volume":"74","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6430-567X","authenticated-orcid":false,"given":"Agelos","family":"Georgakopoulos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,14]]},"reference":[{"key":"696_CR1","unstructured":"Adiprasito, K.,\u00a0Pat\u00e1kov\u00e1, Z.: A higher-dimensional version of F\u00e1ry\u2019s theorem. arxiv:2404.12265"},{"issue":"1","key":"696_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0166-218X(84)90073-8","volume":"8","author":"M Aigner","year":"1984","unstructured":"Aigner, M., Fromme, M.: A game of cops and robbers. Discrete Appl. Math. 8(1), 1\u201312 (1984)","journal-title":"Discrete Appl. Math."},{"issue":"1","key":"696_CR3","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s11856-011-0158-6","volume":"189","author":"B Bollob\u00e0s","year":"2012","unstructured":"Bollob\u00e0s, B., Leader, I., Walters, M.: Lion and man\u2014can both win? Isr. J. Math. 189(1), 267\u2013286 (2012)","journal-title":"Isr. J. Math."},{"key":"696_CR4","doi-asserted-by":"publisher","DOI":"10.1090\/stml\/061","volume-title":"The Game of Cops and Robbers on Graphs","author":"A Bonato","year":"2011","unstructured":"Bonato, A., Nowakowski, R.J.: The Game of Cops and Robbers on Graphs. American Mathematical Society, Providence, R.I. (2011)"},{"issue":"4","key":"696_CR5","doi-asserted-by":"publisher","first-page":"1987","DOI":"10.1137\/130941328","volume":"28","author":"J Chalopin","year":"2014","unstructured":"Chalopin, J., Chepoi, V., Papasoglu, P., Pecatte, T.: Cop and robber game and hyperbolicity. SIAM J. Discret. Math. 28(4), 1987\u20132007 (2014)","journal-title":"SIAM J. Discret. Math."},{"key":"696_CR6","unstructured":"Ir\u0161i\u010d, V.,\u00a0Mohar, B.,\u00a0Wesolek, A.: Cops and Robber game in higher-dimensional manifolds with spherical and Euclidean metric. C.\u00a0R.\u00a0Math.\u00a0Rep.\u00a0Acad.\u00a0Sci.\u00a0Canada, 44(3):50\u201368, (2022)"},{"key":"696_CR7","doi-asserted-by":"crossref","unstructured":"Ir\u0161i\u010d, V.,\u00a0Mohar, B.,\u00a0Wesolek, A.: Cops and robber on hyperbolic manifolds. In: Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications, pp. 615\u2013622 (2023)","DOI":"10.5817\/CZ.MUNI.EUROCOMB23-085"},{"key":"696_CR8","volume-title":"Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization","author":"R Isaacs","year":"1999","unstructured":"Isaacs, R.: Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. Dover, New York (1999)"},{"key":"696_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-2065-0","volume-title":"Differential Games","author":"J Lewin","year":"1994","unstructured":"Lewin, J.: Differential Games. Springer, London (1994)"},{"key":"696_CR10","unstructured":"Mohar, B.: The game of Cops and Robber on geodesic spaces. arXiv:2205.11633"},{"key":"696_CR11","unstructured":"Mohar, B.: Min\u2013max theorem for the game of Cops and Robber on geodesic spaces. arXiv:2112.03018"},{"key":"696_CR12","unstructured":"Mohar, B.: Notes on Cops and Robber game on graphs. arXiv:1710.11281"},{"key":"696_CR13","doi-asserted-by":"crossref","unstructured":"Schr\u00f6der, B.: The Copnumber of a graph is bounded by [3\/2 genus (G)] + 3. In: Categorical Perspectives, pp. 243\u2013263. Springer (2001)","DOI":"10.1007\/978-1-4612-1370-3_14"},{"issue":"1","key":"696_CR14","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1006\/jctb.1993.1027","volume":"58","author":"PD Seymour","year":"1993","unstructured":"Seymour, P.D., Thomas, R.: Graph searching and a min\u2013max theorem for tree-width. J. Combin. Theory (Ser. B) 58(1), 22\u201333 (1993)","journal-title":"J. Combin. Theory (Ser. 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