Cross-caps, triple points and a linking invariant for finitely determined germs
It was recently proved that for finitely determined germs Φ : ( C 2 , 0 ) → ( C 3 , 0 ) the number C ( Φ ) of Whitney umbrella points and the number T ( Φ ) of triple values of a stable deformation are topological invariants. The proof uses the fact that the combination C ( Φ ) - 3 T ( Φ ) is topolo...
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| Veröffentlicht in: | Revista matemática complutense 2024, Vol.37 (1), p.299-319 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | It was recently proved that for finitely determined germs
Φ
:
(
C
2
,
0
)
→
(
C
3
,
0
)
the number
C
(
Φ
)
of Whitney umbrella points and the number
T
(
Φ
)
of triple values of a stable deformation are topological invariants. The proof uses the fact that the combination
C
(
Φ
)
-
3
T
(
Φ
)
is topological since it equals the linking invariant of the associated immersion
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. |
|---|---|
| ISSN: | 1139-1138 1988-2807 |
| DOI: | 10.1007/s13163-022-00455-w |