*The primary source is the seminal 1963 differential-topology article, "Groups of homotopy spheres," by Michel Kervaire and John Milnor.*

OUTLINE for Chirasree Chatterjee

- Definition of homotopy n-sphere Σ.
- Examples given by clutching diffeomorphisms.
*Alternative definition* of the commutative monoid Θ_{n} of homotopy n-spheres, which is simpler than that given in Sections 1–2.- Existence of representation by clutching (n ⩾ 6); relation to the mapping class group of the standard (n-1)-sphere.
- Show that reversing orientation of Σ represents an inverse in Θ
_{n}, using clutching. - The two definitions of the commutative monoids Θ
_{n} agree in dimension n ⩾ 5, using the h-cobordism theorem.