*Presentations for MATH 6980-16, covering Chapter II of Thom's famous 1954 paper on cobordism. Click "More info" to download.*

**Question:** When is a homology class represented by a submanifold?

Sean Corrigan will present the organizer's purely geometric-topological alternative to proving Theorem II.7 without Theorem II.6, as well as to justifying the penultimate paragraph on Page 34. This alternative is an adaptation of Thom's Proof II.1.

The latter material (from Page 34) asserts the (k-1)-connectivity of the Thom spaces MO(k) and MSO(k) and their k-th homotopy groups.

The former material (Theorem II.7) asserts the 2k-connectivity of the stabilization maps MO(k) --> \Omega MO(k+1) and MSO(k) --> \Omega MSO(k+1). From the modern viewpoint, these are the bonding maps in the Thom spectra **MO** and **MSO**.

For continuity, here is a link to the previous talk.