Problem Sets

Resources for Participant Talks

A. Talks to accompany mini-course on Algebraic K-theory

  • Talk A1: Applications of K0 - Wall's finiteness obstruction
    • Wall, Finiteness conditions for CW-complexes (pdf)
    • Wall, Finiteness conditions for CW-complexes II (html)
    • Sections 1-3 of the survey article by Ferry and Ranicki (html)
    • Lecture notes by Lurie (pdf)
  • Talk A2: Applications of K1 - Whitehead torsion and the s-cobordism theorem
    • Milnor, Whitehead torsion (pdf)
    • Slides by Lück (pdf)
    • Lecture notes by Lurie: Part 1 (pdf), Part 2 (pdf)
  • Talk A3: Quillen's Theorems A and B
    • Quillen, Higher Algebraic K-Theory I, Section 1 (pdf)
    • Weibel, The K-Book, Chapter 4 (pdf)
  • Talk A4: Quillen's Q-construction, K-groups of an exact category, and fundamental theorems
    • Quillen, Higher Algebraic K-Theory I, Sections 2-5 (pdf)
    • Weibel, The K-Book, Chapter 4 (pdf)
  • Talk A5: Milnor squares and excision
    • Milnor, An introduction to algebraic K-theory (html)
    • Land and Tamme, On the K-theory of pullbacks (html)

B. Talks to accompany mini-course on Cut-and-Paste K-theory

  • Talk B1: Scissors congruence and the Dehn invariant
    • Jessen, The Algebra of Polyhedra and the Dehn-Sydler Theorem (html)
    • Dupont, Scissors Congruences, Group Homology & Characteristic Classes, Chapter 1 (html) (publisher page)
    • Dupont, Algebra of polytopes and homology of flag complexes(html)
  • Talk B2: Scissors congruence as group homology
    • Dupont, Scissors Congruences, Group Homology & Characteristic Classes, Chapters 2-3 (html) (publisher page)
    • Dupont, Algebra of polytopes and homology of flag complexes(html)
  • Talk B3: Cut-and-paste K-theory of manifolds, and squares K-theory
    • Hoekzema, Merling, Murray, Rovi, Semikina, Cut and paste invariants of manifolds via algebraic K-theory (html)
    • Hoekzema, Rovi, Semikina, A K-theory spectrum for cobordism cut and paste groups (html)

C. Talks to accompany mini-course on Trace Methods

  • Talk C1: Morita invariance of HH and THH
    • For classical Hochschild homology, Morita invariance is discussed in Loday's book, Cyclic Homology
    • For topological Hochschild homology this is discussed in section 6 of Blumberg and Mandell, Localization theorems in topological Hochschild homology and topological cyclic homology (html)
    • An excellent discussion of Morita equivalence in general can be found in Bass's book, Algebraic K-theory
    • Malkiewich summarizes Blumberg and Mandell's argument pictorially here: (pdf)
  • Talk C2: Calculation of THH(Fp)
    • Bökstedt, The topological Hochschild homology of Z and Z/p (pdf)
    • A summary of Bökstedt's argument is given in Section 5.2 of Hesselholt and Madsen, On the K-theory of finite algebras over Witt vectors of perfect fields
    • See also this set of exercises from WCATSS 2012: (pdf)