A geometric classification of immersions of 3-manifolds into 5-space
arXiv:math/0506567 · doi:10.1007/s00229-005-0543-8
Abstract
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.
17 pages