×

Quelques remarques sur les surfaces lagrangiennes de Givental. (Some remarks on Givental’s lagrangian surfaces). (French) Zbl 0728.57020

Summary: We give a new proof of an enumerative formula of Givental about the singularities of certain lagrangian surfaces. The method is to compare these lagrangian surfaces to complex curves which may be desingularized by blowing up. A modulo 4 formula for non-orientable surfaces is also obtained and it is shown how to construct all the Givental lagrangian embeddings by lagrangian surgery.

MSC:

57R90 Other types of cobordism
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Apéry, F., Models of the real projective plane (1987), Vieweg: Vieweg Braucschweig
[2] Arnold, V. I., Cobordismes lagrangiens et legendriens I et II, Funkts. Anal. ego Prilozh., 14, 8-17 (1980), et 4
[3] Audin, M., Fibrés normaux d’immersions en dimension moitié, points doubles d’immersions lagrangiennes et plongements totalement réels, Comment. Math. Helvetic, 63, 593-623 (1988) · Zbl 0666.57024
[4] Givental, A. B., Plongements lagrangiens de surfaces et parapluies de Whitney déployés, Funkts. Anal. ego Prilozh., 20, 35-41 (1986), fasc. 3
[5] Lannes, J., Sur les immersion de Boy, (Madsen; Oliver, Algebraic topology, Aarhus 1982. Algebraic topology, Aarhus 1982, Lecture Notes in Mathematics 1051 (1983)) · Zbl 0547.57024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.