Quasi-linear elliptic differential equations for mappings of manifolds, II

Gerasim Kokarev, Sergei Kuksin

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study questions related to the orientability of the infinite-dimensional moduli spaces formed by solutions of elliptic equations for mappings of manifolds. The principal result states that the first Stiefel-Whitney class of such a moduli space is given by the Z2-spectral flow of the families of linearised operators. Under an additional compactness hypotheses, we develop elements of Morse-Bott theory and express the algebraic number of solutions of a non-homogeneous equation with a generic right-hand side in terms of the Euler characteristic of the space of solutions corresponding to the homogeneous equation. The applications of this include estimates for the number of homotopic maps with prescribed tension field and for the number of the perturbed pseudoholomorphic tori, sharpening some known results. © Springer Science + Business Media B.V. 2007.

Original languageEnglish
Pages (from-to)59-113
Number of pages55
JournalAnnals of Global Analysis and Geometry
Volume31
Issue number1
DOIs
Publication statusPublished - Jan 2007

Keywords

  • Elliptic equations
  • Infinite-dimensional moduli spaces
  • Morse-Bott theory
  • Orientation
  • Spectral flow

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