an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from...

Prior to this construction, non-diffeomorphic smooth structures on spheres – exotic spheres – were already known to exist, although the question of the existence...

quaternions and octonions in dimensions other than 2, 4, and 8. The first exotic spheres ever discovered were seven-dimensional. A polytope in seven dimensions...

transformations of a geometric space Exotic sphere – Smooth manifold that is homeomorphic but not diffeomorphic to a sphere Homology sphere – Topological manifold whose...

Euclidean space R4 Exotic sphere, a differentiable n-manifold, homeomorphic but not diffeomorphic to the ordinary n-sphere Exotic atom, an atom with one...

implies that homotopy spheres in those dimensions are precisely exotic spheres. It is open whether non-trivial smooth homotopy spheres exist in dimension...

from the construction of the exotic spheres, manifolds that are homeomorphic, but not diffeomorphic, to the standard sphere, which can be interpreted as...

especially differential topology, the Gromoll–Meyer sphere is a special seven-dimensional exotic sphere with several unique properties. It is named after...

A sphere equipped with a nonstandard smooth structure is called an exotic sphere. The E8 manifold is an example of a topological manifold that does not...

exotic sphere, referring to any n-sphere with nonstandard differential structure. Kervaire and Milnor initiated the systematic study of exotic spheres by...

topological sphere need not be smooth; if it is smooth, it need not be diffeomorphic to the Euclidean sphere (an exotic sphere). The sphere is the inverse...

Pham (1965). Brieskorn manifolds give examples of exotic spheres, for example the Gromoll–Meyer sphere. Greuel, Gert-Martin; Purkert, Walter (2018). "Life...

radial extension and the success of PL radial extension yield exotic spheres via twisted spheres. Clutching construction Hansen, Vagn Lundsgaard (1989). Braids...

surface Exotic R4 Hirzebruch surface K3 surface For more examples see 4-manifold. Brieskorn manifold Exotic sphere Homology sphere Homotopy sphere Lens space...

intra-national relations between urban centers and rural peripheries are spheres where exoticizing dynamics are at a play, even if, as noted above, these dynamics...

Sphere is a 1987 novel by Michael Crichton, his sixth novel under his own name and his sixteenth overall. It was adapted into the film Sphere in 1998...

seven-dimensional space is anomalously large. The lowest known dimension for an exotic sphere is the seventh dimension. In hyperbolic space, 7 is the highest dimension...

1 up to 20. Spheres with a smooth, i.e. C∞−differential structure not smoothly diffeomorphic to the usual one are known as exotic spheres. It is not currently...

boundary and a sphere, and showing this hypothetical cobordism invalidates certain properties of the Hirzebruch signature theorem. Exotic sphere Gromoll–Meyer...

that are not diffeomorphic. (For more information, see the article on exotic spheres.) However, in 2007 Simon Brendle and Richard Schoen utilized Ricci flow...

spheres—exotic spheres—were already known to exist, although the question of the existence of such structures for the particular case of the 4-sphere...

mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples...

attaching maps are smooth. This is false in higher dimensions; any exotic sphere is the union of a 0-handle and an n-handle. A handlebody can be defined...

they show that the set of exotic spheres of dimension n – specifically the monoid of smooth structures on the standard n-sphere – is isomorphic to the group...

space-filling curves) of positive area. An exotic sphere is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. At the time of their discovery...

Hilbert-Smith conjecture Mapping class group Orbifolds Examples Exotic sphere Homology sphere Lens space I-bundle topology glossary List of topology topics...

(including any of the pariahs). The exotic sphere S 61 {\displaystyle S^{61}} is the last odd-dimensional sphere to contain a unique smooth structure;...

along their boundary so that the result is an exotic sphere homeomorphic but not diffeomorphic to a 7-sphere. However, there is a canonical way to choose...

manifolds. John Milnor discovered that some spheres have more than one smooth structure—see Exotic sphere and Donaldson's theorem. Michel Kervaire exhibited...

1007/s12220-020-00395-1 Ekholm, Tobias, Thomas Kragh, and Ivan Smith. "Lagrangian exotic spheres." Journal of Topology and Analysis 8.03 (2016): 375-397. https://doi...