Deloopings of the spaces of long embeddings

Keiichi Sakai. "Deloopings of the spaces of long embeddings." Fundamenta Mathematicae 227.1 (2014): 27-34. <http://eudml.org/doc/282983>.

@article{KeiichiSakai2014,
abstract = {The homotopy fiber of the inclusion from the long embedding space to the long immersion space is known to be an iterated based loop space (if the codimension is greater than two). In this paper we deloop the homotopy fiber to obtain the topological Stiefel manifold, combining results of Lashof and of Lees. We also give a delooping of the long embedding space, which can be regarded as a version of Morlet-Burghelea-Lashof's delooping of the diffeomorphism group of the disk relative to the boundary. As a corollary, we show that the homotopy fiber is weakly equivalent to a space on which the framed little disks operad acts possibly nontrivially, and hence its rational homology is a (higher) BV-algebra in a stable range of dimensions.},
author = {Keiichi Sakai},
journal = {Fundamenta Mathematicae},
keywords = {spaces of long embeddings; topological Stiefel manifolds; BV structures; spinning},
language = {eng},
number = {1},
pages = {27-34},
title = {Deloopings of the spaces of long embeddings},
url = {http://eudml.org/doc/282983},
volume = {227},
year = {2014},
}

TY - JOUR
AU - Keiichi Sakai
TI - Deloopings of the spaces of long embeddings
JO - Fundamenta Mathematicae
PY - 2014
VL - 227
IS - 1
SP - 27
EP - 34
AB - The homotopy fiber of the inclusion from the long embedding space to the long immersion space is known to be an iterated based loop space (if the codimension is greater than two). In this paper we deloop the homotopy fiber to obtain the topological Stiefel manifold, combining results of Lashof and of Lees. We also give a delooping of the long embedding space, which can be regarded as a version of Morlet-Burghelea-Lashof's delooping of the diffeomorphism group of the disk relative to the boundary. As a corollary, we show that the homotopy fiber is weakly equivalent to a space on which the framed little disks operad acts possibly nontrivially, and hence its rational homology is a (higher) BV-algebra in a stable range of dimensions.
LA - eng
KW - spaces of long embeddings; topological Stiefel manifolds; BV structures; spinning
UR - http://eudml.org/doc/282983
ER -