Related Spaces
More examples of open, contractible 3-manifolds may be constructed by proceeding in similar fashion and picking different embeddings of Ti+1 in Ti in the iterative process. Each embedding should be an unknotted solid torus in the 3-sphere. The essential properties are that the meridian of Ti should be null-homotopic in the complement of Ti+1, and in addition the longitude of Ti+1 should not be null-homotopic in Ti − Ti+1. Another variation is to pick several subtori at each stage instead of just one. The cones over some of these continua appear as the complements of Casson handles in a 4-ball.
The dogbone space is not a manifold but its product with R1 is homeomorphic to R4.
Read more about this topic: Whitehead Manifold
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“Gambling is closely related to theft, and lewdness to murder.”
—Chinese proverb.
“When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
—Blaise Pascal (1623–1662)