Bonn THDM 2013: Exercises

• Background
• Schedule
• Program

This page lists the exercises for consideration during the Summer School on High Dimensional Manifolds.

Participants are encouraged to work on the solution page of each and to contribute to the discussion pages of both exercises and solutions.

1 Exercise session 1

1.1 Exercise session 1a

• K-group, zeroth (Ex)
• Finitely dominated CW complexes (Ex)
• Homology braid I (Ex)
• Homology braid II (Ex)
• Dehn surgery (Ex)
• Structure set (Ex)

1.2 Exercise session 1b

• Surgery obstruction, signature (Ex)
• Surgery obstruction, Arf-invariant (Ex)
• E8-form (Ex)
• Even dimensional surgery obstruction (Ex)

2 Exercise session 2

• K-group, first (Ex)
• Whitehead torsion (Ex)
• Reidemeister torsion (Ex)
• K-group, all (Ex)
• Generator sets and the kernel formation (Ex)
• Kernel formation (Ex)
• Presentations (Ex)
• Homotopy spheres I (Ex)
• Homotopy spheres II (Ex)
• Homotopy spheres III (Ex)
• Inertia group I (Ex)
• Manifolds cross a circle (Ex)

3 Exercise session 3

• Equivariant maps (Ex)
• Forms and chain complexes I (Ex)
• Structured chain complexes (Ex)
• Structured chain complexes V (Ex)
• Structured chain complexes III (Ex)
• Suspension of a symmetric complex (Ex)
• Structured chain complexes IV (Ex)
• S-duality III (Ex)
• Formations and chain complexes I (Ex)
• Boundaries of symmetric complexes (Ex)
• Homotopy spheres I (Ex)
• Homotopy spheres II (Ex)
• Homotopy spheres III (Ex)
• Inertia group I (Ex)
• Manifolds cross a circle (Ex)

4 Exercise session 4

• Kervaire-Milnor Braid (Ex)
• Inertia group II (Ex)
• Smoothings of products (Ex)
• Homotopy spheres IV (Ex)
• Kappa classes (Ex)
• Normal maps and submanifolds (Ex)
• Splitting invariants (Ex)
• Chain duality I (Ex)
• Chain duality II (Ex)
• Chain duality III (Ex)
• Chain duality IV (Ex)
• Chain duality V (Ex)
• Chain duality VI (Ex)
• Smash product (Ex)
• K-groups of oriented surface groups (Ex)
• Idempotents in group rings (Ex)
• Borel conjecture in dimensions 1 and 2 (Ex)
• Classifying spaces for proper group actions (Ex)
• Equivariant homology (Ex)
• K-group, zeroth II (Ex)