Topology Atlas | Conferences

Knots in Washington XXVIII; Follow up to Workshop on Knots and Quantum Computing (December, 2007 at UT Dallas)
February 27 - March 1, 2009
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UTD), Jozef H. Przytycki (GWU), Vish Ramakrishna (UTD), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Kouki Taniyama (Waseda and GWU), Hao Wu (GWU)

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Projective knots
by
Rama Mishra
Indian Institute of Science Education and Research, Pune, India
Coauthors: Alan Durfee and Don Oshea

It is of interest to study knots in an arbitrary 3-manifold. Here we are interested in knots in the real projective 3-space RP3. As the unit circle S1 and the projective line RP1 are homeomorphic, a knot in RP3 may be regarded as a smooth embedding of RP1 in RP3. Embeddings of RP1 in RP3 are studied in algebraic geometry as a projective map of RP1 in RP3, which is a smooth embedding. We call them projective knots. We have seen that knots in S3 can be represented as a one point compactification of polynomial embeddings of R to R3 known as Polynomial knots. In this case we will see that knots in RP3 are represented by projective closure of embeddings given by rational functions from R to R3. In this talk we will discuss various questions related to projective knots.

Date received: February 19, 2009

Copyright © 2009 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cayk-08.