Geometry & Topology Volume 30, issue 5 (2026)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Quantitative bordism over acyclic groups and Cheeger–Gromov $\rho$-invariants

Jae Choon Cha and Geunho Lim

Geometry & Topology 30 (2026) 1899–1929

DOI: 10.2140/gt.2026.30.1899

Bibliography

1	M F Atiyah, R Bott, A Lefschetz fixed point formula for elliptic complexes, II : Applications, Ann. of Math. (2) 88 (1968) 451 MR232406
2	M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, II, Math. Proc. Cambridge Philos. Soc. 78 (1975) 405 MR397798
3	G Baumslag, E Dyer, A Heller, The topology of discrete groups, J. Pure Appl. Algebra 16 (1980) 1 MR549702
4	J D Boissonnat, R Dyer, A Ghosh, Delaunay triangulation of manifolds, Found. Comput. Math. 18 (2018) 399 MR3777784
5	D Calegari, scl, 20, Math. Soc. Japan (2009) MR2527432
6	J C Cha, Complexity of surgery manifolds and Cheeger–Gromov invariants, Int. Math. Res. Not. 2016 (2016) 5603 MR3567253
7	J C Cha, A topological approach to Cheeger–Gromov universal bounds for von Neumann ρ-invariants, Comm. Pure Appl. Math. 69 (2016) 1154 MR3493628
8	J Cheeger, M Gromov, Bounds on the von Neumann dimension of L²-cohomology and the Gauss–Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985) 1 MR806699
9	J Cheeger, M Gromov, On the characteristic numbers of complete manifolds of bounded curvature and finite volume, from: "Differential geometry and complex analysis" (editors I Chavel, H M Farkas), Springer (1985) 115 MR780040
10	T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and L²-signatures, Ann. of Math. (2) 157 (2003) 433 MR1973052
11	M Culler, Using surfaces to solve equations in free groups, Topology 20 (1981) 133 MR605653
12	M Gromov, Quantitative homotopy theory, from: "Prospects in mathematics" (editor H Rossi), Amer. Math. Soc. (1999) 45 MR1660471
13	M Gromov, L Guth, Generalizations of the Kolmogorov–Barzdin embedding estimates, Duke Math. J. 161 (2012) 2549 MR2988903
14	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
15	M W Hirsch, B Mazur, Smoothings of piecewise linear manifolds, 80, Princeton Univ. Press (1974) MR415630
16	J F P Hudson, Piecewise linear topology, W A Benjamin (1969) MR248844
17	W Jaco, J H Rubinstein, S Tillmann, ℤ₂-Thurston norm and complexity of 3-manifolds, Math. Ann. 356 (2013) 1 MR3038119
18	D M Kan, W P Thurston, Every connected space has the homology of a K(π,1), Topology 15 (1976) 253 MR413089
19	G Lim, Enhanced bounds for rho-invariants for both general and spherical 3-manifolds, J. Topol. Anal. 16 (2024) 409 MR4770561
20	G Lim, S Weinberger, Bounds on Cheeger–Gromov invariants and simplicial complexity of triangulated manifolds, J. Reine Angew. Math. 808 (2024) 271 MR4708122
21	C Livingston, The stable 4-genus of knots, Algebr. Geom. Topol. 10 (2010) 2191 MR2745668
22	W Lück, L²-invariants : theory and applications to geometry and K-theory, 44, Springer (2002) MR1926649
23	R C Lyndon, M Newman, Commutators as products of squares, Proc. Amer. Math. Soc. 39 (1973) 267 MR314997
24	S Mac Lane, Homology, Band 114, Springer (1963) MR156879
25	F Manin, B Tshishiku, S Weinberger, Quantitative PL bordism, (2023) arXiv:2311.16389
26	J Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. (2) 65 (1957) 357 MR84138
27	M Ramachandran, von Neumann index theorems for manifolds with boundary, J. Differential Geom. 38 (1993) 315 MR1237487
28	H Wilton, Acyclic group and finite cw-complex, MathOverflow answer (2020)