Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.508748
Title: Topology of closed 1-forms on manifolds with boundary
Author: Li, Tieqiang Tan
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2009
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Abstract:
The 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. One fruitful direction of the generalisation of the theory is to look at the zeros of a closed 1-form which can be viewed locally as a real function up to an additive constant, initiated by S.P. Novikov, see [32] and [33]. 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. On the other hand, the topology of a space, e.g. 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 [25] and [26]. M. Farber in [9], [10], [11] and [12] 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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.508748  DOI: Not available
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