Insight in the Rumin Cohomology and Orientability Properties of the Heisenberg Group

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http://hdl.handle.net/10138/337124

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Canarecci , G 2018 , ' Insight in the Rumin Cohomology and Orientability Properties of the Heisenberg Group ' , University of Helsinki . < http://hdl.handle.net/10138/260962 >

Title: Insight in the Rumin Cohomology and Orientability Properties of the Heisenberg Group
Author: Canarecci, Giovanni
Other contributor: Holopainen, Ilkka
Contributor organization: Department of Mathematics and Statistics
Doctoral Programme in Mathematics and Statistics
Geometric Analysis and Partial Differential Equations
Publisher: University of Helsinki
Date: 2018-11-08
Language: eng
Number of pages: 111
URI: http://hdl.handle.net/10138/337124
Abstract: 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 Mobius 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.
Subject: 111 Mathematics
Heisenberg group
sub-Riemannian geometry
Differential geometry
Rumin cohomology
Heisenberg-orientability
Usage restriction: openAccess
Self-archived version: publishedVersion


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