Rational homology ribbon cobordism is a partial order
Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 245-253
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We show that ribbon rational homology cobordism is a partial order within the class of irreducible 3-manifolds. This makes essential use of the methods recently employed by Ian Agol to show that ribbon knot concordance is a partial order.

DOI : 10.2140/agt.2025.25.245
Keywords: ribbon cobordism, ribbon homology, representation varieties, 3-manifolds

Friedl, Stefan  1   ; Misev, Filip  1   ; Zentner, Raphael  1

1 Fakultät für Mathematik, Universität Regensburg, Regensburg, Germany
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Friedl, Stefan; Misev, Filip; Zentner, Raphael. Rational homology ribbon cobordism is a partial order. Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 245-253. doi: 10.2140/agt.2025.25.245

[1] I Agol, Ribbon concordance of knots is a partial ordering, Commun. Am. Math. Soc. 2 (2022) 374 | DOI

[2] M Aschenbrenner, S Friedl, H Wilton, 3-manifold groups, Eur. Math. Soc. (2015) | DOI

[3] A Daemi, T Lidman, D S Vela-Vick, C M M Wong, Ribbon homology cobordisms, Adv. Math. 408 (2022) 108580 | DOI

[4] M Gerstenhaber, O S Rothaus, The solution of sets of equations in groups, Proc. Nat. Acad. Sci. U.S.A. 48 (1962) 1531 | DOI

[5] C M Gordon, Ribbon concordance of knots in the 3-sphere, Math. Ann. 257 (1981) 157 | DOI

[6] J Hempel, Residual finiteness for 3-manifolds, from: "Combinatorial group theory and topology", Ann. of Math. Stud. 111, Princeton Univ. Press (1987) 379 | DOI

[7] M Huber, Ribbon cobordisms between lens spaces, Pacific J. Math. 315 (2021) 111 | DOI

[8] M Huber, Ribbon cobordisms as a partial order, Math. Res. Lett. 30 (2023) 1511 | DOI

[9] P Orlik, Seifert manifolds, 291, Springer (1972) | DOI

[10] P Scott, There are no fake Seifert fibre spaces with infinite π1, Ann. of Math. 117 (1983) 35 | DOI

[11] F Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 | DOI

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