Projective Links and Their Invariants
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
This thesis consists of two papers about knots and links in the real projective space RP3. We present an algorithm to unknot diagrammatically knots and links in RP3. We extend two classical polynomial invariants of links in R3 to links in RP3.
In the first paper, the notion of descending diagram is extended from links in R3 to nonoriented links in RP3. With the help of this extended notion, any nonoriented diagram of a projective link can be unknotted with some crossing changes. It is also shown that the notion of descending diagram cannot be extended to oriented projective links.
In the second paper, Homfly and Kauffman skein modules of the real projective space are computed. Both modules are free and generated by an infinite set of links, described in the paper. This explicit computation gives an extension of the Homfly and Kauffman polynomial invariants of links in R3 to links in RP3. It is also shown that the extended Homfly and Kauffman polynomials allow to measure how far a projective link is from being affine.
Place, publisher, year, edition, pages
Uppsala: Matematiska institutionen , 2004. , 76 p.
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 37
Algebra and geometry, Real projective space, skein modules, Homfly polynomial, Kauffman polynomial, descending link diagram
Algebra och geometri
IdentifiersURN: urn:nbn:se:uu:diva-4519ISBN: 91-506-1765-6OAI: oai:DiVA.org:uu-4519DiVA: diva2:165001
2004-09-27, Room 347, Building 2, Polacksbacken, 13:15
Przytycki, Jozef, Professor
Viro, Oleg, Professor
List of papers