Volume 8, issue 4 (2008)

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

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

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
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Cobordisms of maps with singularities of given class

Yoshifumi Ando

Algebraic & Geometric Topology 8 (2008) 1989–2029
Bibliography
1 Y Ando, Smooth maps with singularities of bounded $\mathcal{K}$–codimensions arXiv:math.GT/0704.0115
2 Y Ando, The homotopy type of the space consisting of regular jets and folding jets in $J^2(n,n)$, Japan. J. Math. $($N.S.$)$ 24 (1998) 169 MR1630137
3 Y Ando, Fold-maps and the space of base point preserving maps of spheres, J. Math. Kyoto Univ. 41 (2001) 693 MR1891672
4 Y Ando, Folding maps and the surgery theory on manifolds, J. Math. Soc. Japan 53 (2001) 357 MR1815139
5 Y Ando, Invariants of fold-maps via stable homotopy groups, Publ. Res. Inst. Math. Sci. 38 (2002) 397 MR1903746
6 Y Ando, Existence theorems of fold-maps, Japan. J. Math. $($N.S.$)$ 30 (2004) 29 MR2070370
7 Y Ando, Smooth maps having only singularities with Boardman symbol $(1,0)$, Topology Appl. 142 (2004) 205 MR2071303
8 Y Ando, Stable homotopy groups of spheres and higher singularities, J. Math. Kyoto Univ. 46 (2006) 147 MR2260821
9 Y Ando, A homotopy principle for maps with prescribed Thom–Boardman singularities, Trans. Amer. Math. Soc. 359 (2007) 489 MR2255183
10 Y Ando, The homotopy principle for maps with singularities of given $\mathcal K$–invariant class, J. Math. Soc. Japan 59 (2007) 557 MR2326177
11 M F Atiyah, Bordism and cobordism, Proc. Cambridge Philos. Soc. 57 (1961) 200 MR0126856
12 M F Atiyah, Thom complexes, Proc. London Math. Soc. $(3)$ 11 (1961) 291 MR0131880
13 J M Boardman, Singularities of differentiable maps, Inst. Hautes Études Sci. Publ. Math. (1967) 21 MR0231390
14 O Burlet, G de Rham, Sur certaines applications génériques d'une variété close à $3$ dimensions dans le plan, Enseignement Math. $(2)$ 20 (1974) 275 MR0365594
15 H Cartan, S Eilenberg, Homological algebra, Princeton University Press (1956) MR0077480
16 D S Chess, Singularity theory and configuration space models of $\Omega^nS^n$ of nonconnected spaces, Topology Appl. 25 (1987) 313 MR889874
17 P E Conner, E E Floyd, Differentiable periodic maps, Ergebnisse der Math. und ihrer Grenzgebiete, N. F. 33, Academic Press (1964) MR0176478
18 J Eliashberg, Singularities of folding type, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970) 1110 MR0278321
19 J Eliashberg, Surgery of singularities of smooth mappings, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972) 1321 MR0339261
20 J Eliashberg, Cobordisme des solutions de relations différentielles, from: "South Rhone seminar on geometry, I (Lyon, 1983)", Travaux en Cours, Hermann (1984) 17 MR753850
21 S D Feit, $k$–mersions of manifolds, Acta Math. 122 (1969) 173 MR0243541
22 M L Gromov, Stable mappings of foliations into manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969) 707 MR0263103
23 M L Gromov, A topological technique for the construction of solutions of differential equations and inequalities, from: "Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2", Gauthier-Villars (1971) 221 MR0420697
24 M L Gromov, Partial differential relations, Ergebnisse der Math. und ihrer Grenzgebiete [Results in Math. and Related Areas] (3) 9, Springer (1986) MR864505
25 M W Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959) 242 MR0119214
26 K Ikegami, O Saeki, Cobordism group of Morse functions on surfaces, J. Math. Soc. Japan 55 (2003) 1081 MR2003761
27 B Kalmár, Cobordism invariants of fold maps arXiv:0709.0350
28 B Kalmár, Cobordism of fold maps, stably framed manifolds and immersions arXiv:0803.1666
29 B Kalmár, Cobordism group of Morse functions on unoriented surfaces, Kyushu J. Math. 59 (2005) 351 MR2188598
30 B Kalmár, Cobordism group of fold maps of oriented $3$–manifolds into the plane, Acta Math. Hungar. 117 (2007) 1 MR2356183
31 M Kazarian, Multisingularities, cobordisms, and enumerative geometry, Uspekhi Mat. Nauk 58 (2003) 29 MR2042262
32 M Kazarian, Thom polynomials, from: "Singularity theory and its applications", Adv. Stud. Pure Math. 43, Math. Soc. Japan (2006) 85 MR2313410
33 S Kobayashi, K Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers John Wiley & Sons (1963) MR0152974
34 J A Lees, On the classification of Lagrange immersions, Duke Math. J. 43 (1976) 217 MR0410764
35 H I Levine, Singularities of differentiable maps, from: "Proceedings of Liverpool Singularities Symposium, (1969/1970)", Lecture Notes in Math. 192, Springer (1971) 1
36 J Martinet, Déploiements versels des applications différentiables et classification des applications stables, from: "Singularités d'applications différentiables (Sém., Plans-sur-Bex, 1975)", Lecture Notes in Math. 535, Springer (1976) 1 MR0649264
37 J N Mather, Stability of $C^{\infty }$ mappings. III. Finitely determined mapgerms, Inst. Hautes Études Sci. Publ. Math. (1968) 279 MR0275459
38 J N Mather, Stability of $C^{\infty }$ mappings. IV. Classification of stable germs by $R$–algebras, Inst. Hautes Études Sci. Publ. Math. (1969) 223 MR0275460
39 J N Mather, On Thom–Boardman singularities, from: "Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971)", Academic Press (1973) 233 MR0353359
40 A Phillips, Submersions of open manifolds, Topology 6 (1967) 171 MR0208611
41 A du Plessis, Maps without certain singularities, Comment. Math. Helv. 50 (1975) 363 MR0397779
42 A du Plessis, Contact-Invariant regularity conditions, from: "Singularités d'applications différentiables (Sém., Plans-sur-Bex, 1975)", Lecture Notes in Math. 535, Springer (1976) 205 MR0482811
43 A du Plessis, Homotopy classification of regular sections, Compositio Math. 32 (1976) 301 MR0413163
44 R Rimányi, A Szücs, Pontrjagin–Thom–type construction for maps with singularities, Topology 37 (1998) 1177 MR1632908
45 R Sadykov, Bordism groups of solutions to differential relations arXiv:math.AT/0608460
46 R Sadykov, Bordism groups of special generic mappings, Proc. Amer. Math. Soc. 133 (2005) 931 MR2113946
47 O Saeki, Topology of special generic maps into $\mathbf{R}^3$, Mat. Contemp. 5 (1993) 161 MR1305180
48 O Saeki, Topology of singular fibers of differentiable maps, Lecture Notes in Math. 1854, Springer (2004) MR2106689
49 O Saeki, K Sakuma, On special generic maps into $\mathbf{R}^3$, Pacific J. Math. 184 (1998) 175 MR1626540
50 J P Serre, Groupes d'homotopie et classes de groupes abéliens, Ann. of Math. $(2)$ 58 (1953) 258 MR0059548
51 S Smale, The classification of immersions of spheres in Euclidean spaces, Ann. of Math. $(2)$ 69 (1959) 327 MR0105117
52 E H Spanier, Function spaces and duality, Ann. of Math. $(2)$ 70 (1959) 338 MR0107862
53 E H Spanier, Algebraic topology, McGraw-Hill Book Co. (1966) MR0210112
54 N Steenrod, The topology of fibre bundles, Princeton Math. Series 14, Princeton University Press (1951) MR0039258
55 R E Stong, Notes on cobordism theory, Math. notes, Princeton University Press (1968) MR0248858
56 A Szűcs, Cobordism of singular maps, Geom. Topol. (2008) 2379
57 R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17 MR0061823