Abstract
AbstractIt was recently proved that for finitely determined germs $$ \Phi : ( \mathbb C^2, 0) \rightarrow ( \mathbb C^3, 0) $$
Φ
:
(
C
2
,
0
)
→
(
C
3
,
0
)
the number $$C(\Phi )$$
C
(
Φ
)
of Whitney umbrella points and the number $$T(\Phi )$$
T
(
Φ
)
of triple values of a stable deformation are topological invariants. The proof uses the fact that the combination $$C(\Phi )-3T(\Phi )$$
C
(
Φ
)
-
3
T
(
Φ
)
is topological since it equals the linking invariant of the associated immersion $$S^3 \looparrowright S^5$$
S
3
↬
S
5
introduced by Ekholm and Szűcs. We provide a new, direct proof for this equality. We also clarify the relation between various definitions of the linking invariant.
Funder
National Research, Development and Innovation Office
Publisher
Springer Science and Business Media LLC