K-theory and applications

Glasgow topology learning seminar

This is the homepage for the topology learning seminar running in Semester 2 of 2023. The aim is to learn about algebraic K-theory and its applications to topology, including controlled K-theory. To begin with, we will work through Milnor's book and take detours if necessary.

The course is aimed at graduate students and postdocs, although anyone is welcome.

The organisers for this seminar are Daniel Galvin and Mark Powell. The talks will be given by the participants.

Schedule

The talks will be held on Thursday from 1300-1400 in 311B.

• 1. February 16th - Introduction and motivation / Projective modules and K_0 (Csaba Nagy)
• 2. February 23rd - Dedekind domains (Csaba Nagy)
• 3. March 2nd - Constructing projective modules (Mark Powell)
• 4. March 9th - K_1 and the Whitehead group (Daniel Galvin)
• 5. March 16th - Whitehead torsion (Daniel Galvin)
• 6. March 23rd - The exact sequence associated with an ideal (Michelle Daher)

Notes

The talks will be typed up and compiled into a set of notes which will be updated as the term progresses.

Link: version last updated March 17th.

Contact Details

d.galvin.1@research.gla.ac.uk

mark.powell@glasgow.ac.uk

References

• Introduction to algebraic K-theory by Milnor. This is the primary reference we will be following to begin with.
• Algebraic K-theory by Bass.
• Algebraic K-theory by Srinivas.
• Whitehead torsion by Milnor. A detailed account of Whitehead torsion, a K-theoretic invariant.
• Algebraic and geometric surgery by Ranicki. Chaptor 8 of this includes an account of K_1, the Whitehead group and Whitehead torsion.
• ...and more to come.