Forms on Manifolds with Boundary
723KbAbstractThe topological structure of a manifold can be eectively revealed by studying the critical points of a nice function assigned on it. This is the essential motivation of Morse theory and many of its generalisations from a modern viewpoint. Novikov, see hermes tray replica uk
 and . Extensive literatures have been devoted to the study of so called Novikov theory on closed manifolds, which consists of interesting objects such as Novikov complex, Morse Novikov inequalities and Novikov ring. a manifold, provides vital information on the number of the critical points of a function. Along this line, a whole dierent approach was suggested in the 1930s by Lusternik and Schnirelman  and . M. Farber in , ,  and  generalised this concept with respect to a closed 1 form, and used it to study the critical points and existence of homoclinic cycles on a closed manifold in much more degenerate settings. This thesis combines the two aspects in the context of closed 1 forms and attempts a systematic treatment on smooth compact manifolds with boundary in the sense that the transversality assumptions on the boundary is consistent thoroughly. Overall, the thesis employs a geometric approach to the generalisation of the existing results.