Algebraic K-Theory and Manifold Topology
Jacob Lurie
Lecture notes.Course Website http://www.math.harvard.edu/∼lurie/281.html
Prerequisites Familiarity with the machinery of modern algebraic topology (simplicial sets,
spectra, ...).
Several other topics (such as piecewise linear topology, microbundles, im-
mersion theory, the language of quasi-categories) will receive a cursory review as we need
them. A high level of mathematical sophistication will be assumed.Possible Topics
• Wall’s Finiteness Obstruction
• Simple homotopy equivalences and Whitehead torsion.
• Polyhedra and simple maps; “higher” simple homotopy theory
• Waldhausen’s algebraic K-theory of spaces
• Assembly; the “parametrized index theorem” of Dwyer-Weiss-Williams.
• Regular neighborhood theory.
• Piecewise linear manifolds, microbundles, and immersion theory
• The parametrized (stable) s-cobordism theorem
• Concordance spaces and the Hatcher spectral sequence
• Hilbert cube manifolds and infinite-dimensional topology
Prerequisites Familiarity with the machinery of modern algebraic topology (simplicial sets,
spectra, ...).
Several other topics (such as piecewise linear topology, microbundles, im-
mersion theory, the language of quasi-categories) will receive a cursory review as we need
them. A high level of mathematical sophistication will be assumed.Possible Topics
• Wall’s Finiteness Obstruction
• Simple homotopy equivalences and Whitehead torsion.
• Polyhedra and simple maps; “higher” simple homotopy theory
• Waldhausen’s algebraic K-theory of spaces
• Assembly; the “parametrized index theorem” of Dwyer-Weiss-Williams.
• Regular neighborhood theory.
• Piecewise linear manifolds, microbundles, and immersion theory
• The parametrized (stable) s-cobordism theorem
• Concordance spaces and the Hatcher spectral sequence
• Hilbert cube manifolds and infinite-dimensional topology