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

Chirasree will do Items 5 & 6 from Lecture 01, thus completing a modern approach to Sections 1–2 of the paper.

OUTLINE for Gerrit Smith

- Definition of an abstract manifold being
*stably parallelizable;* the standard n-sphere necessarily satisfies this property. - Why stabilizing once was enough (Lemma 3.5); a survey of the machine from algebraic topology called
*obstruction theory.* - Why the notion in Item 1 is equivalent to
*parallelizable* for manifolds-with-boundary (Lemma 3.4). - An equivalent notion for embedded manifolds (Lemma 3.3).
- The three-case proof that any homotopy n-sphere is stably parallelizable (Theorem 3.1). This is independent of Items 2–4, which were merely remarks on Item 1.