A geometric classification of immersions of 3-manifolds into 5-space

Details A geometric classification of immersions of 3-manifolds into 5-space A geometric classification of immersions of 3-manifolds into 5-space

2005-06-28

arxiv.org/abs/math/0506567v1

manuscripta math. 117, 65-83 (2005)

Mathematics

Geometric Topology

17 pages

Scientific paper

10.1007/s00229-005-0543-8

In this paper we define two regular homotopy invariants c and i for immersions of oriented 3-manifolds into R^5 in a geometric manner. The pair (c(f),i(f)) completely describes the regular homotopy class of the immersion f. The invariant i corresponds to the 3-dimensional obstruction that arises from Hirsch-Smale theory and extends the one defined in [10] for immersions with trivial normal bundle.

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