Algebraic & Geometric Topology Volume 10, issue 2 (2010)

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Complexity of PL manifolds

Bruno Martelli

Algebraic & Geometric Topology 10 (2010) 1107–1164

DOI: 10.2140/agt.2010.10.1107

Bibliography

1	E Akin, Manifold phenomena in the theory of polyhedra, Trans. Amer. Math. Soc. 143 (1969) 413 MR0253329
2	S B Alexander, R L Bishop, Spines and homology of thin Riemannian manifolds with boundary, Adv. Math. 155 (2000) 23 MR1789847
3	S B Alexander, R L Bishop, Spines and topology of thin Riemannian manifolds, Trans. Amer. Math. Soc. 355 (2003) 4933 MR1997598
4	M A Armstrong, Transversality for polyhedra, Ann. of Math. $(2)$ 86 (1967) 172 MR0219075
5	I K Babenko, Asymptotic invariants of smooth manifolds, Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992) 707 MR1208148
6	R Benedetti, C Petronio, Lectures on hyperbolic geometry, Universitext, Springer (1992) MR1219310
7	G Besson, G Courtois, S Gallot, Volume et entropie minimale des espaces localement symétriques, Invent. Math. 103 (1991) 417 MR1085114
8	B A Burton, Enumeration of non-orientable $3$–manifolds using face-pairing graphs and union-find, Discrete Comput. Geom. 38 (2007) 527 MR2352707
9	P J Callahan, M V Hildebrand, J R Weeks, A census of cusped hyperbolic $3$–manifolds, Math. Comp. 68 (1999) 321 MR1620219
10	F Costantino, Complexity of $4$–manifolds, Experiment. Math. 15 (2006) 237 MR2253547
11	F Costantino, D Thurston, $3$–manifolds efficiently bound $4$–manifolds, J. Topol. 1 (2008) 703 MR2417451
12	S Eilenberg, J A Zilber, Semi-simplicial complexes and singular homology, Ann. of Math. $(2)$ 51 (1950) 499 MR0035434
13	R Fintushel, R J Stern, Knots, links, and $4$–manifolds, Invent. Math. 134 (1998) 363 MR1650308
14	R Frigerio, B Martelli, C Petronio, Small hyperbolic $3$–manifolds with geodesic boundary, Experiment. Math. 13 (2004) 171 MR2068891
15	R E Gompf, A new construction of symplectic manifolds, Ann. of Math. $(2)$ 142 (1995) 527 MR1356781
16	R E Gompf, A I Stipsicz, $4$–manifolds and Kirby calculus, Graduate Studies in Math. 20, Amer. Math. Soc. (1999) MR1707327
17	M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982) MR686042
18	M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
19	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
20	D Kotschick, Entropies, volumes, and Einstein metrics arXiv:math/040215
21	T Kuessner, Multicomplexes, bounded cohomology and additivity of simplicial volume arXiv:math/0109057
22	A Manning, Topological entropy for geodesic flows, Ann. of Math. $(2)$ 110 (1979) 567 MR554385
23	B Martelli, Four-manifolds with shadow-complexity zero arXiv:0909.0168
24	B Martelli, Links, two-handles, and four-manifolds, Int. Math. Res. Not. (2005) 3595 MR2200121
25	B Martelli, Complexity of $3$-manifolds, from: "Spaces of Kleinian groups" (editors M N., M Sakuma, C Series), London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 91 MR2258746
26	B Martelli, C Petronio, Three-manifolds having complexity at most 9, Experiment. Math. 10 (2001) 207 MR1837672
27	S V Matveev, Special skeletons of piecewise linear manifolds, Mat. Sb. $($N.S.$)$ 92(134) (1973) 282, 344 MR0343285
28	S V Matveev, The theory of the complexity of three-dimensional manifolds, Akad. Nauk Ukrain. SSR Inst. Mat. Preprint (1988) 32 MR982986
29	S V Matveev, Complexity theory of three-dimensional manifolds, Acta Appl. Math. 19 (1990) 101 MR1074221
30	S V Matveev, Tabulation of three-dimensional manifolds, Uspekhi Mat. Nauk 60 (2005) 97 MR2190925
31	S V Matveev, Algorithmic topology and classification of $3$–manifolds, Algorithms and Computation in Math. 9, Springer (2007) MR2341532
32	C McCrory, Cone complexes and PL transversality, Trans. Amer. Math. Soc. 207 (1975) 269 MR0400243
33	G Mikhalkin, Decomposition into pairs-of-pants for complex algebraic hypersurfaces, Topology 43 (2004) 1035 MR2079993
34	H R Morton, Joins of polyhedra, Topology 9 (1970) 243 MR0261587
35	G P Paternain, J Petean, Minimal entropy and collapsing with curvature bounded from below, Invent. Math. 151 (2003) 415 MR1953264
36	C P Rourke, B J Sanderson, Block bundles. I, Ann. of Math. $(2)$ 87 (1968) 1 MR0226645
37	C P Rourke, B J Sanderson, Introduction to piecewise-linear topology, Ergebnisse Math. ihrer Grenzgebiete 69, Springer (1972) MR0350744
38	D A Stone, Stratified polyhedra, Lecture Notes in Math. 252, Springer (1972) MR0372870
39	J H C Whitehead, On $C^1$–complexes, Ann. of Math. $(2)$ 41 (1940) 809 MR0002545