Deloopings of the spaces of long embeddings

• Autorzy: Keiichi Sakai
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57N35: Embeddings and immersions
• 58D10: Spaces of imbeddings and immersions
• 57Q45: Knots and links (in high dimensions)
• 55P50: String topology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 227
• Numer: 1
• Strony: 27-34

Daty

wydano

2014

Twórcy

autor

Keiichi Sakai

• Department of Mathematical Sciences, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano 390-8621, Japan

Identyfikatory

DOI

10.4064/fm227-1-3