caa a22 4500 46324821X CHVBK 20180405153332.0 cr unu---uuuuu 170326e20070101xx s 000 0 eng 10.1007/s10455-006-9034-8 doi (NATIONALLICENCE)springer-10.1007/s10455-006-9034-8 Quasi-linear elliptic differential equations for mappings of manifolds, II [Elektronische Daten] [Gerasim Kokarev, Sergei Kuksin] 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., 2006 Elliptic equations nationallicence Infinite-dimensional moduli spaces nationallicence Orientation nationallicence Spectral flow nationallicence Morse-Bott theory nationallicence Kokarev Gerasim School of Mathematics, The University of Edinburgh, King's Bulidings, Mayfield Road, EH9 3JZ, Edinburgh, UK aut Kuksin Sergei School of Mathematical and Computer Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK aut Annals of Global Analysis and Geometry Kluwer Academic Publishers 31/1(2007-01-01), 59-113 0232-704X 31:1<59 2007 31 10455 https://doi.org/10.1007/s10455-006-9034-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10455-006-9034-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kokarev Gerasim School of Mathematics, The University of Edinburgh, King's Bulidings, Mayfield Road, EH9 3JZ, Edinburgh, UK aut NATIONALLICENCE 700 1- Kuksin Sergei School of Mathematical and Computer Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK aut NATIONALLICENCE 773 0- Annals of Global Analysis and Geometry Kluwer Academic Publishers 31/1(2007-01-01), 59-113 0232-704X 31:1<59 2007 31 10455 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer