Algebraic & Geometric Topology Volume 6, issue 4 (2006)

Download this article
	For screen
	For printing

Recent 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

Widths of surface knots

Yasushi Takeda

Algebraic & Geometric Topology 6 (2006) 1831–1861

DOI: 10.2140/agt.2006.6.1831

Bibliography

1	P M Akhmet’ev, Smooth immersions of manifolds of small dimension, Mat. Sb. 185 (1994) 3 MR1309180
2	S Bleiler, M Scharlemann, A projective plane in $\mathbf{R}^4$ with three critical points is standard. Strongly invertible knots have property $P$, Topology 27 (1988) 519 MR976593
3	V Carrara, J S Carter, M Saito, Singularities of the projections of surfaces in 4-space, Pacific J. Math. 199 (2001) 21 MR1847145
4	V L Carrara, M A S Ruas, O Saeki, Maps of manifolds into the plane which lift to standard embeddings in codimension two, Topology Appl. 110 (2001) 265 MR1807468
5	J S Carter, M Saito, Knotted surfaces and their diagrams, Mathematical Surveys and Monographs 55, American Mathematical Society (1998) MR1487374
6	T Cochran, Ribbon knots in $S^{4}$, J. London Math. Soc. $(2)$ 28 (1983) 563 MR724727
7	T Fukuda, Topology of folds, cusps and Morin singularities, from: "A fête of topology", Academic Press (1988) 331 MR928406
8	D Gabai, Foliations and the topology of $3$-manifolds. III, J. Differential Geom. 26 (1987) 479 MR910018
9	M Golubitsky, V Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics 14, Springer (1973) MR0341518
10	F Hosokawa, A Kawauchi, Proposals for unknotted surfaces in four-spaces, Osaka J. Math. 16 (1979) 233 MR527028
11	S Kamada, Surfaces in $\mathbf{R}^4$ of braid index three are ribbon, J. Knot Theory Ramifications 1 (1992) 137 MR1164113
12	S Kamada, Braid and knot theory in dimension four, Mathematical Surveys and Monographs 95, American Mathematical Society (2002) MR1900979
13	A Kawauchi, On pseudo-ribbon surface-links, J. Knot Theory Ramifications 11 (2002) 1043 MR1941684
14	H I Levine, Mappings of manifolds into the plane, Amer. J. Math. 88 (1966) 357 MR0208609
15	J N Mather, Generic projections, Ann. of Math. $(2)$ 98 (1973) 226 MR0362393
16	O Saeki, Y Takeda, Canceling branch points and cusps on projections of knotted surfaces in 4-space, Proc. Amer. Math. Soc. 132 (2004) 3097 MR2063132
17	M Scharlemann, Smooth spheres in $\mathbf{R}^4$ with four critical points are standard, Invent. Math. 79 (1985) 125 MR774532
18	K Tanaka, Crossing changes for pseudo-ribbon surface-knots, Osaka J. Math. 41 (2004) 877 MR2116343
19	K Tanaka, The braid index of surface-knots and quandle colorings, Illinois J. Math. 49 (2005) 517 MR2164349
20	R Thom, Les singularités des applications différentiables, Ann. Inst. Fourier, Grenoble 6 (1955–1956) 43 MR0087149
21	O J Viro, Local knotting of sub-manifolds, Mat. Sb. (N.S.) 90(132) (1973) 173, 325 MR0370606
22	M Yamamoto, Lifting a generic map from a surface into the plane to an embedding into $4$-space
23	T Yasuda, Crossing and base numbers of ribbon 2-knots, J. Knot Theory Ramifications 10 (2001) 999 MR1867105
24	E C Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965) 471 MR0195085