Sammanfattning
Originalspråk  engelska 

Tilldelande institution 

Handledare 

Tilldelningsdatum  6 nov 2018 
Förlag  
Status  Publicerad  8 nov 2018 
MoEpublikationstyp  G3 Licentiatavhandling 
Vetenskapsgrenar
 111 Matematik
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Insight in the Rumin Cohomology and Orientability Properties of the Heisenberg Group. / Canarecci, Giovanni.
University of Helsinki, 2018. 111 s.Forskningsoutput: Avhandling › Licentiatavhandling
TY  THES
T1  Insight in the Rumin Cohomology and Orientability Properties of the Heisenberg Group
AU  Canarecci, Giovanni
PY  2018/11/8
Y1  2018/11/8
N2  The purpose of this study is to analyse two related topics: the Rumin cohomology and the Horientability 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 Horientability for Hregular surfaces and we prove that Horientability 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 Hregular surface and we use this fact to prove that there exist Hregular nonHorientable surfaces, at least in the case n+1. This opens the possibility for an analysis of Heisenberg currents mod 2.
AB  The purpose of this study is to analyse two related topics: the Rumin cohomology and the Horientability 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 Horientability for Hregular surfaces and we prove that Horientability 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 Hregular surface and we use this fact to prove that there exist Hregular nonHorientable surfaces, at least in the case n+1. This opens the possibility for an analysis of Heisenberg currents mod 2.
KW  111 Mathematics
KW  Heisenberg group
KW  subRiemannian geometry
KW  Differential geometry
KW  Rumin cohomology
KW  Heisenbergorientability
M3  Licenciate's thesis
PB  University of Helsinki
ER 