DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Jin, Gyo-Taek | - |
dc.contributor.advisor | 진교택 | - |
dc.contributor.author | Kim, Hun | - |
dc.contributor.author | 김훈 | - |
dc.date.accessioned | 2011-12-14T04:39:19Z | - |
dc.date.available | 2011-12-14T04:39:19Z | - |
dc.date.issued | 2001 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=169599&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41841 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수학전공, 2001.8, [ [ii], 45 p. ] | - |
dc.description.abstract | An n-lace ℓ (in $R^2$) is the union $ℓ_1∪…∪ℓ_n$ of disjoint simple arcs in $R^2$ such that $∂ℓ_i = {(i,1),(π(i),-1)}$, i = 1, …, n, for some permutation π of {1,2,…,n}. We denote by $L_n$ the set of isotopy classes of n-laces. In this thesis, we investigate planar laces using geometric and algebraic methods. First, using geometric and combinatorial methods we show that there is an one to one correspondence between 1-laces on 1-punctured plane and a set of integer pairs. And we find a relationship between integer pair and cobordism class of 1-laces on 1-punctured plane. We have similar results for 2-laces on $S^2$. For the algebraic method, we use the mapping class group of plane. We obtain the presentation of a subgroup $LM_{2n}$ which acts on planar laces transitively as a subgroup of mapping class group. And we have the presentation of isotropy subgroup $T_n$ of trivial laces. The map β: $L_n→B_n$ is defined geometrically. The preimages of trivial braid are called pseudo trivial laces. We define an algebraic map b: LM_{2n}→B_n$ which factors through $L_n$. Then using the map b, we find the subgroup $PL_{2n}$ which acts on pseudo trivial laces transitively. We have devised an algorithm of cap reducing process to detect pseudo trivial laces. Cap reducing process is a sequence of finger moves which do not change braid type. We can deform a lace to a lower lace by cap reducing process. We show that a given lace is pseudo trivial if and only if the lower lace obtained by cap reducing process is trivial. Finally, we have a relationship between lace links and pseudo trivial laces. Any n-bridge n-components link can be obtained from pure n-laces. We show that any n-bridge n-components link can be obtained from pseudo trivial n-laces. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | planar laces | - |
dc.subject | braid | - |
dc.subject | 고리 | - |
dc.subject | mapping class group | - |
dc.subject | knot | - |
dc.subject | link | - |
dc.subject | 평면 레이스 | - |
dc.subject | 땋임 | - |
dc.subject | 사상류군 | - |
dc.subject | 매듭 | - |
dc.title | On planar laces | - |
dc.title.alternative | 평면 레이스에 대하여 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 169599/325007 | - |
dc.description.department | 한국과학기술원 : 수학전공, | - |
dc.identifier.uid | 000955105 | - |
dc.contributor.localauthor | Jin, Gyo-Taek | - |
dc.contributor.localauthor | 진교택 | - |
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