Isomorphisms of Lie algebras of vector fields
The author gives a survey of the history of isospectral manifolds that are non-isometric discussing the work of Milnor, Vignéras, Sunada, and de Turck and Gordon. She describes the construction of continuous isospectral deformations as introduced by Gordon, Wilson, De Turck et al. She also discusses the construction of isospectral plane domains due to Gordon, Webb, and Wolpert. Some new examples of isospectral non-isometric manifolds are given.
This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [18, 19], while this survey focuses on the main ideas and examples.
The purpose of this paper is to put together a large amount of results on the conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results, examples and an historical overview of the subject. But, it is also a reference text on the topic that contains proofs of a large part of the results on this question. Some proofs as well as few results are new. Furthermore, the text, being addressed to non-experts, is as...