Volume Conjecture and its generalizations

体积猜想指出，通过研究结的有色琼斯多项式的某种渐近行为，可以告诉我们结补的体积。它是由R. Kashaev， J. Murakami和主要研究者提出的。现在这个猜想被推广到各种各样的方式，吸引了包括理论物理学家在内的许多研究者。在这项研究中，我们解决了部分猜想，给出了更多的推广，并解决了这些推广的一部分。

The volume conjecture states that by studying a certain asymptotic behavior of the colored Jones polynomial of a knot would tell us the volume of the knot complement. It was proposed by R. Kashaev, J. Murakami and the main investigator. Now the conjecture is generalized to various ways and attracts many researchers including theoretical physicists. In this research we solve part of the conjecture, give yet more generalizations, and solve part of these generalizations.