Smooth area preserving isotopies of self transverse immersions of S¹ into R²
Let C and C′ be two smooth self transverse immersions of S1 into R2. BothC and C′ divide the plane into a number of disks and one unbounded component.An isotopy of the plane which takes C to C′ induces a 1-1 correspondence betweenthe disks of C and C′. An obvious necessary condition for there to exi...
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Uppsala universitet, Matematiska institutionen
2009
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ndltd-UPSALLA1-oai-DiVA.org-uu-1125222013-04-10T16:33:31ZSmooth area preserving isotopies of self transverse immersions of S¹ into R²engKarlsson, CeciliaUppsala universitet, Matematiska institutionen2009MATHEMATICSMATEMATIKLet C and C′ be two smooth self transverse immersions of S1 into R2. BothC and C′ divide the plane into a number of disks and one unbounded component.An isotopy of the plane which takes C to C′ induces a 1-1 correspondence betweenthe disks of C and C′. An obvious necessary condition for there to exist an areapreserving isotopy of the plane taking C to C′ is that there exists an isotopy forwhich the area of every disk of C has the same area as the corresponding disk ofC′. In this paper we show that this is also a sufficient condition. Student thesisinfo:eu-repo/semantics/bachelorThesistexthttp://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-112522U.U.D.M. project report ; 2009:25application/pdfinfo:eu-repo/semantics/openAccess |
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NDLTD |
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English |
| format |
Others
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NDLTD |
| topic |
MATHEMATICS MATEMATIK |
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MATHEMATICS MATEMATIK Karlsson, Cecilia Smooth area preserving isotopies of self transverse immersions of S¹ into R² |
| description |
Let C and C′ be two smooth self transverse immersions of S1 into R2. BothC and C′ divide the plane into a number of disks and one unbounded component.An isotopy of the plane which takes C to C′ induces a 1-1 correspondence betweenthe disks of C and C′. An obvious necessary condition for there to exist an areapreserving isotopy of the plane taking C to C′ is that there exists an isotopy forwhich the area of every disk of C has the same area as the corresponding disk ofC′. In this paper we show that this is also a sufficient condition. |
| author |
Karlsson, Cecilia |
| author_facet |
Karlsson, Cecilia |
| author_sort |
Karlsson, Cecilia |
| title |
Smooth area preserving isotopies of self transverse immersions of S¹ into R² |
| title_short |
Smooth area preserving isotopies of self transverse immersions of S¹ into R² |
| title_full |
Smooth area preserving isotopies of self transverse immersions of S¹ into R² |
| title_fullStr |
Smooth area preserving isotopies of self transverse immersions of S¹ into R² |
| title_full_unstemmed |
Smooth area preserving isotopies of self transverse immersions of S¹ into R² |
| title_sort |
smooth area preserving isotopies of self transverse immersions of s¹ into r² |
| publisher |
Uppsala universitet, Matematiska institutionen |
| publishDate |
2009 |
| url |
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-112522 |
| work_keys_str_mv |
AT karlssoncecilia smoothareapreservingisotopiesofselftransverseimmersionsofs1intor2 |
| _version_ |
1716580003367354368 |