Precise Arrhenius law for p-forms: The Witten Laplacian and Morse-Barannikov complex.

Dorian Le Peutrec (1) , Francis Nier (2) , Claude Viterbo (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 CMLS - Centre de Mathématiques Laurent Schwartz

Accurate asymptotic expressions are given for the exponentially small eigenvalues of Witten Laplacians acting on p-forms. The key ingredient, which replaces explicit formulas for global quasimodes in the case p = 0, is Barannikov's presentation of Morse theory.

Mots clés: Morse- Barannikov complex; Exponentially small eigenvalues; Witten Laplacians; Morse- Barannikov complex.

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]; Géométrie différentielle [math.DG]; Topologie algébrique [math.AT]

Dorian Le Peutrec, Francis Nier, Claude Viterbo. Precise Arrhenius law for p-forms: The Witten Laplacian and Morse-Barannikov complex.. 2011. ⟨hal-00596959⟩