András Szűcs

Regular homotopy classes of immersions of 3-manifolds into 5-space

Abstract We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into 5-space. These are analogues of the geometric formulae for the Smale invariants due to Ekholm and the second author. As a corollary, we show that two embeddings into 5-space of a closed oriented 3-manifold with no 2-torsion in the second cohomology are regularly homotopic if and only if they have Seifert surfaces with the same signature. We also show that there exist two embeddings

On the number of triple points of an immersed surface with boundary

F_0

Two Theorems of Rokhlin

and of the 3-torus T3 with the following properties: (1) is regularly homotopic to F8 for some immersion , and (2) the immersion h as above cannot be chosen from a regular homotopy class containing an embedding.

Multiplicative properties of Morin maps

Given a generic immersionf:S1→S2 of a circle into the sphere, we find the best possible lower estimation for the number of triple points of a generic immersionF: (M, S1)→(B3,S2) extendingf, whereM is an oriented surface with boundary ∂M=S1,B3 is the 3-dimensional ball with boundaryS2.

On double points of immersed surfaces

AbstractTwo theorems due to V. A. Rokhlin are proved: the theorem on the third stable homotopy group of spheres:

Cobordism of singular maps

\pi _{n + 3} (S^n ) \approx \mathbb{Z}_{24} {\text{ }}for{\text{ }}n \geqslant {\text{5}}

On the Singularities of Hyperplane Projections of Immersions

; and the theorem on the divisibility by 16 of the signature of a spin 4-manifold. The proofs use immersion theory. Bibliography 17 titles.

Cobordism groups of immersions of oriented manifolds

In the first part of the paper we construct a ring structure on the rational cobordism classes of Morin maps (i. e. smooth generic maps of corank 1). We show that associating to a Morin map its singular strata defines a ring homomorphism to