#### Volume 16, issue 3 (2016)

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Singular fibers of stable maps of $3$–manifolds with boundary into surfaces and their applications

### Osamu Saeki and Takahiro Yamamoto

Algebraic & Geometric Topology 16 (2016) 1379–1402
##### Bibliography
 1 J Damon, The relation between C∞ and topological stability, Bol. Soc. Brasil. Mat. 8 (1977) 1 MR0649254 2 C G Gibson, K Wirthmüller, A A du Plessis, E J N Looijenga, Topological stability of smooth mappings, 552, Springer (1976) MR0436203 3 M Golubitsky, V Guillemin, Stable mappings and their singularities, 14, Springer (1973) MR0341518 4 L F Martins, A C Nabarro, Projections of hypersurfaces in ℝ4 with boundary to planes, Glasg. Math. J. 56 (2014) 149 MR3137856 5 T Ohmoto, Vassiliev complex for contact classes of real smooth map-germs, Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem. 27 (1994) 1 MR1341346 6 A du Plessis, T Wall, The geometry of topological stability, 9, Clarendon Press (1995) MR1408432 7 O Saeki, Topology of singular fibers of differentiable maps, 1854, Springer (2004) MR2106689 8 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 9 O Saeki, S Takahashi, Visual data mining based on differential topology: a survey, Pac. J. Math. Ind. 6 (2014) MR3404141 10 O Saeki, S Takahashi, D Sakurai, H Y Wu, K Kikuchi, H Carr, D Duke, T Yamamoto, Visualizing multivariate data using singularity theory, from: "The impact of applications on mathematics" (editors M Wakayama, R S Anderssen, J Cheng, Y Fukumoto, R McKibbin, K Polthier, T Takagi, K C Toh), Math. Ind. (Tokyo) 1, Springer (2014) 51 MR3445542 11 O Saeki, T Yamamoto, Singular fibers of stable maps and signatures of 4–manifolds, Geom. Topol. 10 (2006) 359 MR2224462 12 O Saeki, T Yamamoto, Singular fibers and characteristic classes, Topology Appl. 155 (2007) 112 MR2368204 13 O Saeki, T Yamamoto, Co-orientable singular fibers of stable maps of 3–manifolds with boundary into surfaces, Sūrikaisekikenkyūsho Kōkyūroku 1948 (2015) 137 14 N Shibata, On non-singular stable maps of 3–manifolds with boundary into the plane, Hiroshima Math. J. 30 (2000) 415 MR1799298 15 V A Vassilyev, Lagrange and Legendre characteristic classes, 3, Gordon and Breach (1988) MR1065996 16 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 17 T Yamamoto, Euler number formulas in terms of singular fibers of stable maps, from: "Real and complex singularities" (editors A Harris, T Fukui, S Koike), World Sci. (2007) 427 MR2336698 18 T Yamamoto, Singular fibers of two-colored maps and cobordism invariants, Pacific J. Math. 234 (2008) 379 MR2373454