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...
Main Author: | |
---|---|
Format: | Others |
Language: | English |
Published: |
Uppsala universitet, Matematiska institutionen
2009
|
Subjects: | |
Online Access: | http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-112522 |
id |
ndltd-UPSALLA1-oai-DiVA.org-uu-112522 |
---|---|
record_format |
oai_dc |
spelling |
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 |
collection |
NDLTD |
language |
English |
format |
Others
|
sources |
NDLTD |
topic |
MATHEMATICS MATEMATIK |
spellingShingle |
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 |