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2 results on '"formal embeddings"'

1. Fundamental groups of formal Legendrian and horizontal embedding spaces

Author

Fernández Fuertes, Eduardo, Martínez-Aguinaga, Javier, Presas, Francisco, Fernández Fuertes, Eduardo, Martínez-Aguinaga, Javier, and Presas, Francisco

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., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Published
2020

2. Fundamental groups of formal Legendrian and horizontal embedding spaces

Author

Eduardo Fernández, Javier Martínez-Aguinaga, Francisco Presas, Ministerio de Ciencia e Innovación (España), and Eusko Jaurlaritza

Subjects
Pure mathematics, Fundamental group, Matemáticas, 58A17, Space (mathematics), 01 natural sciences, formal embeddings, 0103 physical sciences, FOS: Mathematics, 0101 mathematics, Mathematics::Symplectic Geometry, 57R17, 58A17, 53D10, 57R17, Mathematics, Legendrian knots, Connected component, 010102 general mathematics, Geometría diferencial, 53D10, Mathematics - Symplectic Geometry, Symplectic Geometry (math.SG), Embedding, 010307 mathematical physics, Geometry and Topology, Isomorphism, horizontal knots
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 π-level., The authors are supported by Spanish Research Projects SEV?2015?0554, MTM2016?79400?P and MTM2015?72876?EXP. Fernández is supported by a Master?Severo Ochoa grant and by Beca de Personal Investigador en Formación UCM. MartínezAguinaga is funded by Programa Predoctoral de Formación de Personal Investigador No Doctor del Departamento de Educación del Gobierno Vasco.

Published
2020

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