Algebraic & Geometric Topology Volume 9, issue 4 (2009)

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Bordism groups of solutions to differential relations

Rustam Sadykov

Algebraic & Geometric Topology 9 (2009) 2311–2347

DOI: 10.2140/agt.2009.9.2311

Bibliography

1	Y Ando, Smooth maps with singularities of bounded 𝒦–codimensions arXiv:0704.0115v2
2	Y Ando, Folding maps and the surgery theory on manifolds, J. Math. Soc. Japan 53 (2001) 357 MR1815139
3	Y Ando, Existence theorems of fold-maps, Japan. J. Math. (N.S.) 30 (2004) 29 MR2070370
4	Y Ando, A homotopy principle for maps with prescribed Thom–Boardman singularities, Trans. Amer. Math. Soc. 359 (2007) 489 MR2255183
5	Y Ando, The homotopy principle for maps with singularities of given 𝒦–invariant class, J. Math. Soc. Japan 59 (2007) 557 MR2326177
6	Y Ando, Cobordisms of maps with singularities of given class, Algebr. Geom. Topol. 8 (2008) 1989 MR2449006
7	J M Boardman, Singularities of differentiable maps, Inst. Hautes Études Sci. Publ. Math. (1967) 21 MR0231390
8	D S Chess, Singularity theory and configuration space models of ΩⁿSⁿ of nonconnected spaces, Topology Appl. 25 (1987) 313 MR889874
9	Y Eliashberg, On singularities of folding type, Math. USSR, Izv. 4 (1970) 1119
10	Y Eliashberg, Surgery of singularities of smooth mappings, Math. USSR, Izv. 6 (1972) 1302
11	Y Eliashberg, Cobordisme des solutions de relations différentielles, from: "South Rhone seminar on geometry, I (Lyon, 1983)" (editors P Dazord, N Desolneux-Moulis), Travaux en Cours, Hermann (1984) 17 MR753850
12	Y Eliashberg, S Galatius, Homotopy theory of compactified moduli space, Oberwolfach Report 13/2006 (2006) 761
13	Y Eliashberg, N M Mishachev, Wrinkling of smooth mappings. III. Foliations of codimension greater than one, Topol. Methods Nonlinear Anal. 11 (1998) 321 MR1659446
14	Y Eliashberg, N M Mishachev, Introduction to the h–principle, 48, Amer. Math. Soc. (2002) MR1909245
15	L M Fehér, R Rimányi, Calculation of Thom polynomials and other cohomological obstructions for group actions, from: "Real and complex singularities" (editors T Gaffney, M A S Ruas), Contemp. Math. 354, Amer. Math. Soc. (2004) 69 MR2087805
16	D B Fuks, Quillenization and bordism, Funkcional. Anal. i Priložen. 8 (1974) 36 MR0343301
17	S Galatius, U Tillmann, I Madsen, M Weiss, The homotopy type of the cobordism category, Acta Math. 202 (2009) 195 MR2506750
18	M 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
19	M Gromov, Partial differential relations, 9, Springer (1986) MR864505
20	M Gromov, Y Eliashberg, Elimination of singularities of smooth mappings, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971) 600 MR0301748
21	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
22	K Ikegami, Cobordism group of Morse functions on manifolds, Hiroshima Math. J. 34 (2004) 211 MR2086843
23	K Ikegami, O Saeki, Cobordism group of Morse functions on surfaces, J. Math. Soc. Japan 55 (2003) 1081 MR2003761
24	K Jänich, Symmetry properties of singularities of C^∞–functions, Math. Ann. 238 (1978) 147 MR512820
25	B Kalmár, Fold cobordisms and stable homotopy groups arXiv:0704.3147
26	B Kalmár, Cobordism group of Morse functions on unoriented surfaces, Kyushu J. Math. 59 (2005) 351 MR2188598
27	M Kazarian, Kharakteristicheskie classy v teorii osobennostej, Habilitation thesis (2003)
28	M Kazarian, Multisingularities, cobordisms, and enumerative geometry, Uspekhi Mat. Nauk 58 (2003) 29 MR2042262
29	M Kazarian, Thom polynomials, from: "Singularity theory and its applications" (editors S Izumiya, G Ishikawa, H Tokunaga, I Shimada, T Sano), Adv. Stud. Pure Math. 43, Math. Soc. Japan (2006) 85 MR2313410
30	S O Kochman, Bordism, stable homotopy and Adams spectral sequences, 7, Amer. Math. Soc. (1996) MR1407034
31	U Koschorke, Vector fields and other vector bundle morphisms—a singularity approach, 847, Springer (1981) MR611333
32	I Madsen, M Weiss, The stable moduli space of Riemann surfaces : Mumford’s conjecture, Ann. of Math. (2) 165 (2007) 843 MR2335797
33	N M Mishachev, Y Eliashberg, Surgery of singularities of foliations, Funkcional. Anal. i Priložen. 11 (1977) 43, 96 MR0474326
34	A Phillips, Submersions of open manifolds, Topology 6 (1967) 171 MR0208611
35	A du Plessis, Maps without certain singularities, Comment. Math. Helv. 50 (1975) 363 MR0397779
36	A du Plessis, Contact-Invariant regularity conditions, from: "Singularités d’applications différentiables (Sém., Plans-sur-Bex, 1975)" (editors O Burlet, F Ronga), Lecture Notes in Math. 535, Springer (1976) 205 MR0482811
37	R Rimányi, Thom polynomials, symmetries and incidences of singularities, Invent. Math. 143 (2001) 499 MR1817643
38	R Rimányi, A Szücs, Pontrjagin–Thom-type construction for maps with singularities, Topology 37 (1998) 1177 MR1632908
39	C Rourke, B Sanderson, The compression theorem. I, Geom. Topol. 5 (2001) 399 MR1833749
40	Y B Rudyak, On Thom spectra, orientability, and cobordism, , Springer (1998) MR1627486
41	R Sadykov, Bordism groups of solutions to differential relations arXiv:math/0608460
42	R Sadykov, Singular cobordism categories arXiv:0804.1267
43	R Sadykov, Bordism groups of special generic mappings, Proc. Amer. Math. Soc. 133 (2005) 931 MR2113946
44	R Sadykov, Cobordism groups of Morin maps, Preprint (2008)
45	O Saeki, Cobordism groups of special generic functions and groups of homotopy spheres, Japan. J. Math. (N.S.) 28 (2002) 287 MR1947905
46	O Saeki, T Yamamoto, Singular fibers and characteristic classes, Topology Appl. 155 (2007) 112 MR2368204
47	D Spring, Convex integration theory. Solutions to the h–principle in geometry and topology, 92, Birkhäuser Verlag (1998) MR1488424
48	R E Stong, Notes on cobordism theory, , Princeton Univ. Press (1968) MR0248858
49	R M Switzer, Algebraic topology—homotopy and homology, 212, Springer (1975) MR0385836
50	A Szűcs, Elimination of singularities by cobordism, from: "Real and complex singularities" (editors T Gaffney, M A S Ruas), Contemp. Math. 354, Amer. Math. Soc. (2004) 301 MR2088057
51	A Szűcs, Cobordism of singular maps, Geom. Topol. 12 (2008) 2379 MR2443969
52	W P Thurston, The theory of foliations of codimension greater than one, Comment. Math. Helv. 49 (1974) 214 MR0370619
53	W P Thurston, Existence of codimension-one foliations, Ann. of Math. (2) 104 (1976) 249 MR0425985
54	C T C Wall, A second note on symmetry of singularities, Bull. London Math. Soc. 12 (1980) 347 MR587705
55	R Wells, Cobordism groups of immersions, Topology 5 (1966) 281 MR0196760