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arXiv · 1809.10401

The index of Toeplitz operators on compact Lie groups and simply connected closed 3-manifolds

Duván Cardona
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Abstract

In this paper we use the notion of operator-valued symbol in order to compute the index of Toeplitz operators on compact Lie groups. Our approach combines the Connes index theorem and the infinite-dimensional operator-valued symbolic calculus of Ruzhansky-Turunen. We also give applications to the index of Toeplitz operators on simply connected closed $3$-manifolds $\mathbb{M}\simeq \mathbb{S}^3\simeq \textnormal{SU}(2) ,$ by using, as a fundamental tool, the Poincar\'e theorem (see Perelman [31,32,33,34])

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Duván Cardona. 2018-09-27. The index of Toeplitz operators on compact Lie groups and simply connected closed 3-manifolds. https://arxiv.org/abs/1809.10401

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