Algebraic & Geometric Topology Volume 23, issue 7 (2023)

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On a problem of Hopf for circle bundles over aspherical manifolds with hyperbolic fundamental groups

Christoforos Neofytidis

Algebraic & Geometric Topology 23 (2023) 3205–3220

DOI: 10.2140/agt.2023.23.3205

Bibliography

1	A Bartels, W Lück, The Borel conjecture for hyperbolic and CAT(0)–groups, Ann. of Math. 175 (2012) 631 MR2993750
2	A Bartels, W Lück, H Reich, The K–theoretic Farrell–Jones conjecture for hyperbolic groups, Invent. Math. 172 (2008) 29 MR2385666
3	I Belegradek, On co-Hopfian nilpotent groups, Bull. London Math. Soc. 35 (2003) 805 MR2000027
4	A Borel, On periodic maps of certain K(π,1), from: "Œuvres : collected papers", Springer (1983) 57 MR725854
5	M Bridson, A Hinkkanen, G Martin, Quasiregular self-mappings of manifolds and word hyperbolic groups, Compos. Math. 143 (2007) 1613 MR2371385
6	R Brooks, W Goldman, Volumes in Seifert space, Duke Math. J. 51 (1984) 529 MR757951
7	M Bucher-Karlsson, Simplicial volume of locally symmetric spaces covered by SL₃ℝ∕SO(3), Geom. Dedicata 125 (2007) 203 MR2322549
8	P E Conner, F Raymond, Actions of compact Lie groups on aspherical manifolds, from: "Topology of manifolds" (editors J C Cantrell, J Edwards C. H.), Markham (1970) 227 MR271958
9	D Crowley, C Löh, Functorial seminorms on singular homology and (in)flexible manifolds, Algebr. Geom. Topol. 15 (2015) 1453 MR3361142
10	P Derbez, S Wang, Graph manifolds have virtually positive Seifert volume, J. Lond. Math. Soc. 86 (2012) 17 MR2959293
11	M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982) 5 MR686042
12	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
13	J C Hausmann, Geometric Hopfian and non-Hopfian situations, from: "Geometry and topology" (editors C McCrory, T Shifrin), Lecture Notes in Pure and Appl. Math. 105, Dekker (1987) 157 MR873292
14	R Kirby, Problems in low-dimensional topology, from: "Geometric topology" (editor R Kirby), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
15	D Kotschick, C Löh, Fundamental classes not representable by products, J. Lond. Math. Soc. 79 (2009) 545 MR2506686
16	J F Lafont, B Schmidt, Simplicial volume of closed locally symmetric spaces of non-compact type, Acta Math. 197 (2006) 129 MR2285319
17	W Lück, L²–invariants : theory and applications to geometry and K–theory, 44, Springer (2002) MR1926649
18	W Lück, Survey on aspherical manifolds, from: "European Congress of Mathematics" (editors A Ran, H te Riele, J Wiegerinck), Eur. Math. Soc. (2010) 53 MR2648321
19	A Maltsev, On isomorphic matrix representations of infinite groups, Mat. Sbornik N.S. 8(50) (1940) 405 MR3420
20	I Mineyev, Straightening and bounded cohomology of hyperbolic groups, Geom. Funct. Anal. 11 (2001) 807 MR1866802
21	I Mineyev, Bounded cohomology characterizes hyperbolic groups, Q. J. Math. 53 (2002) 59 MR1887670
22	C Neofytidis, Fundamental groups of aspherical manifolds and maps of non-zero degree, Groups Geom. Dyn. 12 (2018) 637 MR3813205
23	C Neofytidis, Ordering Thurston’s geometries by maps of nonzero degree, J. Topol. Anal. 10 (2018) 853 MR3881042
24	B H Neumann, On a problem of Hopf, J. London Math. Soc. 28 (1953) 351 MR55996
25	M S Raghunathan, Discrete subgroups of Lie groups, 68, Springer (1972) MR507234
26	Z Sela, Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups, II, Geom. Funct. Anal. 7 (1997) 561 MR1466338
27	Z Sela, Endomorphisms of hyperbolic groups, I : The Hopf property, Topology 38 (1999) 301 MR1660337
28	D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 269 MR646078
29	S C Wang, The existence of maps of nonzero degree between aspherical 3–manifolds, Math. Z. 208 (1991) 147 MR1125739
30	S C Wang, The π₁–injectivity of self-maps of nonzero degree on 3–manifolds, Math. Ann. 297 (1993) 171 MR1238414