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

Volume 25
Issue 8, 4437–5174
Issue 7, 3789–4436
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

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