Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Topology and geometry of flagness and beltness of simple handlebodies

Zhi Lü and Lisu Wu

Algebraic & Geometric Topology 25 (2025) 55–106
Bibliography
1 A Adem, J Leida, Y Ruan, Orbifolds and stringy topology, 171, Cambridge Univ. Press (2007) MR2359514
2 E M Andreev, Convex polyhedra of finite volume in Lobačevskiĭ space, Mat. Sb. 83(125) (1970) 256 MR273510
3 A Bahri, M Bendersky, F R Cohen, S Gitler, Decompositions of the polyhedral product functor with applications to moment-angle complexes and related spaces, Proc. Natl. Acad. Sci. USA 106 (2009) 12241 MR2539227
4 A Bahri, D Notbohm, S Sarkar, J Song, On integral cohomology of certain orbifolds, Int. Math. Res. Not. 2021 (2021) 4140 MR4230390
5 Y Barreto, S López de Medrano, A Verjovsky, Some open book and contact structures on moment-angle manifolds, Bol. Soc. Mat. Mex. 23 (2017) 423 MR3633142
6 F Bosio, L Meersseman, Real quadrics in n, complex manifolds and convex polytopes, Acta Math. 197 (2006) 53 MR2285318
7 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
8 V M Buchstaber, N Y Erokhovets, M Masuda, T E Panov, S Pak, Cohomological rigidity of manifolds defined by 3-dimensional polytopes, Uspekhi Mat. Nauk 72 (2017) 3 MR3635437
9 V M Buchstaber, T E Panov, Toric topology, 204, Amer. Math. Soc. (2015) MR3363157
10 X Cao, Z Lü, Möbius transform, moment-angle complexes and Halperin–Carlsson conjecture, J. Algebraic Combin. 35 (2012) 121 MR2873100
11 B Chen, Z Lü, L Yu, Self-dual binary codes from small covers and simple polytopes, Algebr. Geom. Topol. 18 (2018) 2729 MR3848398
12 W Chen, A homotopy theory of orbispaces, preprint (2001) arXiv:math/0102020
13 W Chen, Y Ruan, A new cohomology theory of orbifold, Comm. Math. Phys. 248 (2004) 1 MR2104605
14 S Choi, H Park, Small covers over wedges of polygons, J. Math. Soc. Japan 71 (2019) 739 MR3984241
15 V I Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk 33 (1978) 85 MR495499
16 V I Danilov, Birational geometry of three-dimensional toric varieties, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982) 971 MR675526
17 M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983) 293 MR690848
18 M W Davis, The geometry and topology of Coxeter groups, 32, Princeton Univ. Press (2008) MR2360474
19 M W Davis, Lectures on orbifolds and reflection groups, from: "Transformation groups and moduli spaces of curves", Adv. Lect. Math. 16, International (2011) 63 MR2883685
20 M W Davis, Right-angularity, flag complexes, asphericity, Geom. Dedicata 159 (2012) 239 MR2944529
21 M W Davis, A L Edmonds, Euler characteristics of generalized Haken manifolds, Algebr. Geom. Topol. 14 (2014) 3701 MR3302976
22 M W Davis, T Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991) 417 MR1104531
23 M W Davis, T Januszkiewicz, Hyperbolization of polyhedra, J. Differential Geom. 34 (1991) 347 MR1131435
24 M Davis, T Januszkiewicz, R Scott, Nonpositive curvature of blow-ups, Selecta Math. 4 (1998) 491 MR1668119
25 M Davis, T Januszkiewicz, R Scott, Fundamental groups of blow-ups, Adv. Math. 177 (2003) 115 MR1985196
26 B Everitt, J G Ratcliffe, S T Tschantz, Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel, Math. Ann. 354 (2012) 871 MR2983072
27 S Fomin, M Shapiro, D Thurston, Cluster algebras and triangulated surfaces, I : Cluster complexes, Acta Math. 201 (2008) 83 MR2448067
28 B Foozwell, H Rubinstein, Introduction to the theory of Haken n-manifolds, from: "Topology and geometry in dimension three", Contemp. Math. 560, Amer. Math. Soc. (2011) 71 MR2866924
29 W Fulton, Introduction to toric varieties, 131, Princeton Univ. Press (1993) MR1234037
30 A Garrison, R Scott, Small covers of the dodecahedron and the 120-cell, Proc. Amer. Math. Soc. 131 (2003) 963 MR1937435
31 S Gitler, S López de Medrano, Intersections of quadrics, moment-angle manifolds and connected sums, Geom. Topol. 17 (2013) 1497 MR3073929
32 M Gromov, Hyperbolic groups, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
33 M Gromov, H B Lawson Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980) 423 MR577131
34 M Gromov, H B Lawson Jr., Spin and scalar curvature in the presence of a fundamental group, I, Ann. of Math. 111 (1980) 209 MR569070
35 M Gromov, H B Lawson Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983) 83 MR720933
36 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
37 M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
38 S Kuroki, M Masuda, L Yu, Small covers, infra-solvmanifolds and curvature, Forum Math. 27 (2015) 2981 MR3393385
39 H B Lawson Jr., S T Yau, Compact manifolds of nonpositive curvature, J. Differential Geom. 7 (1972) 211 MR334083
40 B Leeb, 3-manifolds with(out) metrics of nonpositive curvature, Invent. Math. 122 (1995) 277 MR1358977
41 Z Lü, Graphs of 2-torus actions, from: "Toric topology", Contemp. Math. 460, Amer. Math. Soc. (2008) 261 MR2428361
42 Z Lü, M Masuda, Equivariant classification of 2-torus manifolds, Colloq. Math. 115 (2009) 171 MR2491742
43 Z Lü, Q Tan, Small covers and the equivariant bordism classification of 2-torus manifolds, Int. Math. Res. Not. 2014 (2014) 6756 MR3291639
44 R C Lyndon, P E Schupp, Combinatorial group theory, 89, Springer (1977) MR577064
45 G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973) MR385004
46 G Moussong, Hyperbolic Coxeter groups, PhD thesis, Ohio State University (1988) MR2636665
47 H Nakayama, Y Nishimura, The orientability of small covers and coloring simple polytopes, Osaka J. Math. 42 (2005) 243 MR2132014
48 D Notbohm, Colorings of simplicial complexes and vector bundles over Davis–Januszkiewicz spaces, Math. Z. 266 (2010) 399 MR2678634
49 J P Otal, Thurston’s hyperbolization of Haken manifolds, from: "Surveys in differential geometry, III", International (1998) 77 MR1677888
50 P Petersen, Riemannian geometry, 171, Springer (2016) MR3469435
51 M Poddar, S Sarkar, On quasitoric orbifolds, Osaka J. Math. 47 (2010) 1055 MR2791564
52 A V Pogorelov, A regular partition of Lobachevskian space, Mat. Zametki 1 (1967) 3 MR208458
53 R K W Roeder, J H Hubbard, W D Dunbar, Andreev’s theorem on hyperbolic polyhedra, Ann. Inst. Fourier (Grenoble) 57 (2007) 825 MR2336832
54 I Satake, The Gauss–Bonnet theorem for V -manifolds, J. Math. Soc. Japan 9 (1957) 464 MR95520
55 R Schoen, S T Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. 110 (1979) 127 MR541332
56 R Schoen, S T Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979) 159 MR535700
57 S Stolz, Simply connected manifolds of positive scalar curvature, Ann. of Math. 136 (1992) 511 MR1189863
58 W P Thurston, Three-dimensional geometry and topology, I, 35, Princeton Univ. Press (1997) MR1435975
59 È B Vinberg, O V Shvartsman, Discrete groups of motions of spaces of constant curvature, from: "Geometry, II", Encycl. Math. Sci. 29, Springer (1993) 139 MR1254933
60 F Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR224099
61 L Wu, L Yu, Fundamental groups of small covers revisited, Int. Math. Res. Not. 2021 (2021) 7262 MR4259148