Fundamental groups of formal Legendrian and horizontal embedding spaces

Fernández, Eduardo¹ ; Martínez-Aguinaga, Javier¹ ; Presas, Francisco²

¹Departamento de Álgebra, Geometría y Topología, Facultad de Matemáticas, Universidad Complutense de Madrid, and Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Madrid, Spain
²Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Madrid, Spain

Algebraic and Geometric Topology, Tome 20 (2020) no. 7, pp. 3219-3312

Résumé

We compute the fundamental group of each connected component of the space of formal Legendrian embeddings in ℝ3. We use it to show that previous examples in the literature of nontrivial loops of Legendrian embeddings are already nontrivial at the formal level. Likewise, we compute the fundamental group of the different connected components of the space of formal horizontal embeddings into the standard Engel ℝ4. We check that the natural inclusion of the space of horizontal embeddings into the space of formal horizontal embeddings induces an isomorphism at π1–level.

Détail

DOI : 10.2140/agt.2020.20.3219

Keywords: Legendrian knots, horizontal knots, formal embeddings

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