Precise Arrhenius Law for p-forms: The Witten Laplacian and Morse–Barannikov Complex

By Dorian Le Peutrec, Francis Nier, C. Viterbo. 2011

51 citations recorded by the source corpus.

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 in Barannikov (Adv Soviet Math 21:93–115, 1994).

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/27591c13cc248159f0c3177ee027a95ec0e84b1d

Citations in the corpus

• Persistent homology and Floer-Novikov theory (2015, unknown): “(f) spanned by the xi,yi,zi having ℓ≤ λ(indeed the latter is clearly a subspace of Cλ∗, but Proposition 5.5 implies that their dimensions are the same). Now the treatment of the Barannikov complex in [LNV13] involves separating the critical values cof finto three types, where ǫrepresents a small pos”