Universidad Complutense de Madrid
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Fundamental groups of formal Legendrian and horizontal embedding spaces

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Fernández Fuertes, Eduardo and Martínez-Aguinaga, Javier and Presas, Francisco (2020) Fundamental groups of formal Legendrian and horizontal embedding spaces. Algebraic & Geometric Topology, 20 (7). pp. 3219-3312. ISSN 1472-2747

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Official URL: https://msp.org/agt/2020/20-7/p01.xhtml



Abstract

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 [Pi]1 –level.


Item Type:Article
Uncontrolled Keywords:Legendrian knots, horizontal knots, formal embeddings
Palabras clave (otros idiomas):Puntos legendrianos, Puntos de Legendrian, Geometría diferencial
Subjects:Sciences > Mathematics
Sciences > Mathematics > Differential geometry
ID Code:63552
Deposited On:14 Jan 2021 11:35
Last Modified:14 Jan 2021 15:24

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