Some Topics in Geometric Topology II

Kawamura, Kazuhiro

doi:10.2991/978-94-6239-024-9_15

Recent Progress in General Topology III 2013

DOI: 10.2991/978-94-6239-024-9_15

|View full text |Cite

Some Topics in Geometric Topology II

Kazuhiro Kawamura

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 123 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Characterization and topological rigidity of Nöbeling manifolds

Nagórko¹

2012

Memoirs of the AMS

View full text Add to dashboard Cite

We develop a theory of Nöbeling manifolds similar to the theory of Hilbert space manifolds. We show that it reflects the theory of Menger manifolds developed by M. Bestvina [8] and is its counterpart in the realm of complete spaces. In particular we prove the Nöbeling manifold characterization conjecture.We define the n-dimensional universal Nöbeling space ν n to be the subset of R 2n+1 consisting of all points with at most n rational coordinates. To enable comparison with the infinite dimensional case we let ν ∞ denote the Hilbert space. We define an ndimensional Nöbeling manifold to be a Polish space locally homeomorphic to ν n . The following theorem for n = ∞ is the characterization theorem of H. Toruńczyk [36]. We establish it for n < ∞, where it was known as the Nöbeling manifold characterization conjecture.Characterization theorem An n-dimensional Polish ANE(n)-space is a Nöbeling manifold if and only if it is strongly universal in dimension n.The following theorem was proved by D. W. Henderson and R. Schori [23] for n = ∞. We establish it in the finite dimensional case.Topological rigidity theorem. Two n-dimensional Nöbeling manifolds are homeomorphic if and only if they are n-homotopy equivalent.We also establish the open embedding theorem, the Z-set unknotting theorem, the local Z-set unknotting theorem and the sum theorem for Nöbeling manifolds.

show abstract

Characterization and topological rigidity of Nöbeling manifolds

Nagórko¹

2012

Memoirs of the AMS

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Some Topics in Geometric Topology II

Cited by 1 publication

References 123 publications

Characterization and topological rigidity of Nöbeling manifolds

Characterization and topological rigidity of Nöbeling manifolds

Contact Info

Product

Resources

About