Applications of quantum invariants in low dimensional topology

Applications of Tqft Invariants in Low Dimensional Topology

In this short note we give lower bounds for the Heegaard genus of 3-manifolds using various TQFT in 2+1 dimensions. We also study the large k limit and the large G limit of our lower bounds, using a conjecture relating the various combinatorial and physical TQFTs. We also prove, assuming this conjecture, that the HOMFLY polynomial of a framed knot in S 3 along with all of its cables distinguish...

Problems in Low-dimensional Topology

Four-dimensional topology is in an unsettled state: a great deal is known, but the largest-scale patterns and basic unifying themes are not yet clear. Kirby has recently completed a massive review of low-dimensional problems [Kirby], and many of the results assembled there are complicated and incomplete. In this paper the focus is on a shorter list of \tool" questions, whose solution could unif...

Low - dimensional Topology 57

Applications of Quantum Dots in Cell Tracking

Tracking cells after transplantation is always one the main concerns of researchers in the field of regenerative medicine. Finding a tracer with long stability and low cytotoxicity can be considered as a solution for this issue. Semiconductor nanocrystals, also called quantum dots (QDs), have unique photophysical properties which make them as suitable candidate in this setting. Broad-range exci...

Topology Changes in ( 2 + 1 ) - Dimensional Quantum

February 3, 1998 Topology Changes in (2+1)-Dimensional Quantum Gravity Yoshihisa FUJIWARA, Saburo HIGUCHI1 , Akio HOSOYA2 , Takashi MISHIMA3 and Masaru SIINO Department of Physics, Tokyo Institute of Technology, Oh-Okayama Meguro-ku, Tokyo 152, Japan ABSTRACT We study topology changing processes in (2+1)-dimensional quantum gravity with negative cosmological constant. By playing the `gluing-man...