Dogbone space
In geometric topology, the dogbone space, constructed by {{harvs|txt|authorlink=R. H. Bing|first=R. H.|last=Bing|year=1957}}, is a quotient space of three-dimensional Euclidean space such that all inverse images of points are points or tame arcs, yet it is not homeomorphic to . The name "dogbone space" refers to a fanciful resemblance between some of the diagrams of genus 2 surfaces in R. H. Bing's paper and a dog bone. {{harvtxt|Bing|1959}} showed that the product of the dogbone space with is homeomorphic to .
Although the dogbone space is not a manifold, it is a generalized homological manifold and a homotopy manifold.
See also
- List of topologies
- Whitehead manifold, a contractible 3-manifold not homeomorphic to .
References
- {{Citation|author1-link=Robert Daverman | last1=Daverman | first1=Robert J. | title=Decompositions of manifolds | journal=Geom. Topol. Monogr. | url=https://www.ams.org/bookstore-getitem/item=chel-362.h | isbn=978-0-8218-4372-7 | mr=2341468 | year=2007| volume=9 | pages=7–15 | doi=10.1090/chel/362| arxiv=0903.3055}}
- {{Citation | last1=Bing | first1=R. H. | authorlink = R. H. Bing | title=A decomposition of E3 into points and tame arcs such that the decomposition space is topologically different from E3 | jstor=1970058 | mr=0092961 |doi=10.2307/1970058 | year=1957 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=65 | issue=3 | pages=484–500}}
- {{Citation | last1=Bing | first1=R. H. | authorlink = R. H. Bing | title=The cartesian product of a certain nonmanifold and a line is E4 | jstor=1970322 | mr=0107228 | year=1959 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=70 | issue=3 | pages=399–412 | doi=10.2307/1970322| url=http://projecteuclid.org/euclid.bams/1183522317 }}