More Cappell–Shaneson spheres are standard

By Robert E. Gompf. 2009

50 citations recorded by the source corpus.

Akbulut has recently shown that an infinite family of Cappell‐Shaneson homotopy 4‐spheres is diffeomorphic to the standard 4‐sphere. In the present paper, a different method shows that a strictly larger family is standard. This new approach uses no Kirby calculus except through the relatively simple 1979 paper of Akbulut and Kirby showing that the simplest example with untwisted framing is standard. Instead, hidden symmetries of the original Cappell‐Shaneson construction are exploited. In the course of the proof, an example is given showing that Gluck twists can sometimes be undone using symmetries of fishtail neighborhoods. 57R60

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a74679eb6f51bcd708a3287cf7888054626830e6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Man and machine thinking about the smooth 4-dimensional Poincaré conjecture (2009, background): “However, it is known to be trivial for many 2-knots, such as twist-spun knots [20], [36], doubles of ribbon disks [19], and various 2-knots arising from the Cappell–Shaneson construction (those trivialized in [15], [3] and [17]).”