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Cusp cobordism group of Morse functionsMay 14 2019By a Morse function on a compact manifold with boundary we mean a real-valued function without critical points near the boundary such that its critical points as well as the critical points of its restriction to the boundary are all non-degenerate. For ... More

Singular fibers of stable maps of 3-manifolds with boundary into surfaces and their applicationsSep 19 2015In this paper, we first classify singular fibers of proper $C^\infty$ stable maps of 3-dimensional manifolds with boundary into surfaces. Then, we compute the cohomology groups of the associated universal complex of singular fibers, and obtain certain ... More