Fundamental groups of formal Legendrian and horizontal embedding spaces

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 non trivial loops of Legendrian embeddings are already non trivial 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 this computes the fundamental group of the space of horizontal embeddings as well.

73 pages, 78 figures. Many changes. The statements and the proofs are pretty much the same, but we have improven the readability, reorganized the paper, streamlined some of the arguments, avoided proofs by picture, corrected some computational mistakes and increased a lot the number of pictures

References in corpus (4)

• Legendrian knots, transverse knots and combinatorial Floer homology
• A family of embedding spaces
• The diffeotopy group of S^1 \times S^2 via contact topology
• Horizontal loops in Engel space

Cited by in corpus (1)

• Spaces of tight contact structures in dimension 3