Algebraic & Geometric Topology Volume 20, issue 7 (2020)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Shadows of acyclic $4$–manifolds with sphere boundary

Yuya Koda and Hironobu Naoe

Algebraic & Geometric Topology 20 (2020) 3707–3731

DOI: 10.2140/agt.2020.20.3707

Bibliography

1	U Burri, For a fixed Turaev shadow Jones–Vassiliev invariants depend polynomially on the gleams, Comment. Math. Helv. 72 (1997) 110 MR1456320
2	A Carrega, B Martelli, Shadows, ribbon surfaces, and quantum invariants, Quantum Topol. 8 (2017) 249 MR3659491
3	F Costantino, Shadows and branched shadows of 3 and 4–manifolds, PhD thesis, Scuola Normale Superiore (2004)
4	F Costantino, A short introduction to shadows of 4–manifolds, Fund. Math. 188 (2005) 271 MR2191948
5	F Costantino, Complexity of 4–manifolds, Experiment. Math. 15 (2006) 237 MR2253547
6	F Costantino, Stein domains and branched shadows of 4–manifolds, Geom. Dedicata 121 (2006) 89 MR2276237
7	F Costantino, Branched shadows and complex structures on 4–manifolds, J. Knot Theory Ramifications 17 (2008) 1429 MR2469211
8	F Costantino, R Frigerio, B Martelli, C Petronio, Triangulations of 3–manifolds, hyperbolic relative handlebodies, and Dehn filling, Comment. Math. Helv. 82 (2007) 903 MR2341844
9	F Costantino, D Thurston, 3–manifolds efficiently bound 4–manifolds, J. Topol. 1 (2008) 703 MR2417451
10	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
11	D Gabai, Foliations and the topology of 3–manifolds, III, J. Differential Geom. 26 (1987) 479 MR910018
12	H Ikeda, Acyclic fake surfaces, Topology 10 (1971) 9 MR326735
13	M Ishikawa, Y Koda, Stable maps and branched shadows of 3–manifolds, Math. Ann. 367 (2017) 1819 MR3623239
14	M Ishikawa, H Naoe, Milnor fibration, A’Campo’s divide and Turaev’s shadow, from: "Singularities" (editors M Ishikawa, S Yokura), World Sci. (2020) 95
15	Y Koda, B Martelli, H Naoe, Four-manifolds with shadow-complexity one, preprint (2018) arXiv:1803.06713
16	B Martelli, Links, two-handles, and four-manifolds, Int. Math. Res. Not. 2005 (2005) 3595 MR2200121
17	B Martelli, Four-manifolds with shadow-complexity zero, Int. Math. Res. Not. 2011 (2011) 1268 MR2806506
18	S Matveev, Algorithmic topology and classification of 3–manifolds, 9, Springer (2003) MR1997069
19	H Naoe, Shadows of 4–manifolds with complexity zero and polyhedral collapsing, Proc. Amer. Math. Soc. 145 (2017) 4561 MR3690638
20	H Naoe, Mazur manifolds and corks with small shadow complexities, Osaka J. Math. 55 (2018) 479 MR3824842
21	H Naoe, Corks with large shadow-complexity and exotic four-manifolds, Experiment. Math. (2019)
22	G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
23	G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint (2003) arXiv:math/0307245
24	G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math/0303109
25	A Shumakovitch, Shadow formula for the Vassiliev invariant of degree two, Topology 36 (1997) 449 MR1415598
26	D P Thurston, The algebra of knotted trivalent graphs and Turaev’s shadow world, from: "Invariants of knots and 3–manifolds" (editors T Ohtsuki, T Kohno, T Le, J Murakami, J Roberts, V Turaev), Geom. Topol. Monogr. 4, Geom. Topol. Publ. (2002) 337 MR2048108
27	V G Turaev, Shadow links and face models of statistical mechanics, J. Differential Geom. 36 (1992) 35 MR1168981
28	V G Turaev, Quantum invariants of knots and 3–manifolds, 18, de Gruyter (1994) MR1292673