Insight in the Rumin Cohomology and Orientability Properties of the Heisenberg Group
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http://hdl.handle.net/10138/260962
Title:
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Insight in the Rumin Cohomology and Orientability Properties of the Heisenberg Group |
Author:
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Canarecci, Giovanni
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Contributor:
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University of Helsinki, Faculty of Science, Department of Mathematics and Statistics |
Publisher:
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University of Helsinki |
Date:
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2018-11-08 |
URI:
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http://hdl.handle.net/10138/260962
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Thesis level:
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Licenciate thesis |
Abstract:
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The purpose of this study is to analyse two related topics: the Rumin cohomology and the H-orientability in the Heisenberg group H^n. In the first three chapters we carefully describe the Rumin cohomology with particular emphasis at the second order differential operator D, giving examples in the cases n=1 and n=2. We also show the commutation between all Rumin differential operators and the pullback by a contact map and, more generally, describe pushforward and pullback explicitly in different situations. Differential forms can be used to define the notion of orientability; indeed in the fourth chapter we define the H-orientability for H-regular surfaces and we prove that H-orientability implies standard orientability, while the opposite is not always true. Finally we show that, up to one point, a Möbius strip in H^1 is a H-regular surface and we use this fact to prove that there exist H-regular non-H-orientable surfaces, at least in the case n=1. This opens the possibility for an analysis of Heisenberg currents mod 2. |
Discipline:
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Matematiikka
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Rights:
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This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited. |
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