Algebraic & Geometric Topology Volume 22, issue 6 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

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

Fold cobordisms and a Poincaré–Hopf-type theorem for the signature

Boldizsár Kalmár

Algebraic & Geometric Topology 22 (2022) 2533–2586

DOI: 10.2140/agt.2022.22.2533

Bibliography

1	J C Alexander, S M Kahn, Characteristic number obstructions to fibering oriented and complex manifolds over surfaces, Topology 19 (1980) 265 MR579576
2	Y Ando, Fold-maps and the space of base point preserving maps of spheres, J. Math. Kyoto Univ. 41 (2001) 693 MR1891672
3	Y Ando, Existence theorems of fold-maps, Japan. J. Math. 30 (2004) 29 MR2070370
4	Y Ando, Stable homotopy groups of spheres and higher singularities, J. Math. Kyoto Univ. 46 (2006) 147 MR2260821
5	Y Ando, Cobordisms of maps with singularities of given class, Algebr. Geom. Topol. 8 (2008) 1989 MR2449006
6	R L W Brown, Cobordism and bundles over spheres, Michigan Math. J. 16 (1969) 315 MR250319
7	D Chess, A Poincaré–Hopf type theorem for the de Rham invariant, Bull. Amer. Math. Soc. 3 (1980) 1031 MR585184
8	T Ekholm, A Szűcs, Geometric formulas for Smale invariants of codimension two immersions, Topology 42 (2003) 171 MR1928649
9	T Ekholm, A Szűcs, T Terpai, Cobordisms of fold maps and maps with a prescribed number of cusps, Kyushu J. Math. 61 (2007) 395 MR2362892
10	Y M Eliashberg, Singularities of folding type, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970) 1110 MR0278321
11	D Husemoller, Fibre bundles, 20, Springer (1994) MR1249482
12	K Ikegami, Cobordism group of Morse functions on manifolds, Hiroshima Math. J. 34 (2004) 211 MR2086843
13	K Ikegami, O Saeki, Cobordism group of Morse functions on surfaces, J. Math. Soc. Japan 55 (2003) 1081 MR2003761
14	K Jänich, Symmetry properties of singularities of C^∞–functions, Math. Ann. 238 (1978) 147 MR512820
15	T Kálmán, Stable maps of surfaces into the plane, Topology Appl. 107 (2000) 307 MR1779817
16	B Kalmár, Cobordism group of fold maps of oriented 3-manifolds into the plane, Acta Math. Hungar. 117 (2007) 1 MR2356183
17	B Kalmár, Cobordism invariants of fold maps, from: "Real and complex singularities" (editors M J Saia, J Seade), Contemp. Math. 459, Amer. Math. Soc. (2008) 103 MR2444396
18	B Kalmár, Fold cobordisms and stable homotopy groups, Studia Sci. Math. Hungar. 46 (2009) 437 MR2647931
19	B Kalmár, Fold maps and immersions from the viewpoint of cobordism, Pacific J. Math. 239 (2009) 317 MR2457231
20	B Kalmár, T Terpai, Characteristic classes and existence of singular maps, Trans. Amer. Math. Soc. 364 (2012) 3751 MR2901233
21	U Koschorke, Vector fields and other vector bundle morphisms: a singularity approach, 847, Springer (1981) MR611333
22	H I Levine, Elimination of cusps, Topology 3 (1965) 263 MR176484
23	K C Millett, Generic smooth maps of surfaces, Topology Appl. 18 (1984) 197 MR769291
24	B Ozbagci, Signatures of Lefschetz fibrations, Pacific J. Math. 202 (2002) 99 MR1883972
25	R Rimányi, A Szűcs, Pontrjagin–Thom-type construction for maps with singularities, Topology 37 (1998) 1177 MR1632908
26	R Sadykov, Bordism groups of solutions to differential relations, Algebr. Geom. Topol. 9 (2009) 2311 MR2558312
27	R Sadykov, Fold maps, framed immersions and smooth structures, Trans. Amer. Math. Soc. 364 (2012) 2193 MR2869203
28	O Saeki, Notes on the topology of folds, J. Math. Soc. Japan 44 (1992) 551 MR1167382
29	O Saeki, Fold maps on 4–manifolds, Comment. Math. Helv. 78 (2003) 627 MR1998397
30	O Saeki, Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs, Algebr. Geom. Topol. 6 (2006) 539 MR2220688
31	O Saeki, T Yamamoto, Singular fibers of stable maps and signatures of 4–manifolds, Geom. Topol. 10 (2006) 359 MR2224462
32	E Szabó, A Szűcs, T Terpai, On bordism and cobordism groups of Morin maps, J. Singul. 1 (2010) 134 MR2783151
33	A Szűcs, Analogue of the Thom space for mappings with singularity of type Σ¹, Mat. Sb. 108(150) (1979) 433, 478 MR530320
34	A Szűcs, Cobordism of singular maps, Geom. Topol. 12 (2008) 2379 MR2443969
35	A Szűcs, T Terpai, Homotopy investigation of classifying spaces of cobordisms of singular maps, Acta Math. Hungar. 157 (2019) 489 MR3928787
36	C T C Wall, A second note on symmetry of singularities, Bull. London Math. Soc. 12 (1980) 347 MR587705
37	R Wells, Cobordism groups of immersions, Topology 5 (1966) 281 MR196760
38	T Yamamoto, Classification of singular fibres of stable maps of 4–manifolds into 3–manifolds and its applications, J. Math. Soc. Japan 58 (2006) 721 MR2254408