On Several types of universal invariants of framed links and 3-manifolds derived from Hopf algebras

Autores: Jianjun Paul Tian
Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 142, Nº 1, 2007, págs. 73-92
Idioma: inglés
DOI: 10.1017/s0305004106009674
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Resumen
- Without using representations of quasitriangular ribbon Hopf algebras, Hennings, Kauffman and Radford, Ohtsuki and the author gave different methods to construct invariants of links and 3-manifolds respectively. To understand these different methods and the resultant invariants, we made a comprehensive comparison study in this paper. We show the relations among the universal invariants of framed links defined by these different authors. We also figured out the relations among the resultant invariants of 3-manifolds defined by these different authors. Ignoring the difference by scalar constants and the inversion of Hopf algebras, we found that the invariants of 3-manifolds obtained by these authors are the same or equivalent to each other. Therefore, in a sense, there is only one way to construct invariants of 3-manifolds without using representation theory of Hopf algebras.