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Algebraic K-Theory and Manifold Topology

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Lecture notes.

Author(s): Jacob Lurie
Year: 2014

Language: English

0 Course Syllabus
1 Overview
2 The Wall Finiteness Obstruction
3 Whitehead Torsion
4 Whitehead Torsion, Part II
5 Cell-Like Maps
6 Concordance of Polyhedra
7 Higher Simple Homotopy Theory
8 Fibrations of Polyhedra
9 Fibrations of Simplicial Sets
10 Combinatorial Models for M
11 Equivalence of the Combinatorial Definition
12 Some Loose Ends
13 Homotopy Types and Simple Homotopy Types
14 (Lower) K-theory of ∞-categories
15 The Wall Finiteness Obstruction Revisited
16 Higher K-Theory of ∞-Categories
17 The Additivity Theorem
18 Additive K-Theory
19 Algebraic K-Theory of Ring Spectra
20 Lower K-Groups of Ring Spectra
21 The Algebraic K-Theory of Spaces
22 Constructible Sheaves
23 Universal Local Acyclicity
24 The Assembly Map
25 The Assembly Map, Part II
26 The Assembly Map, Part III
27 Higher Torsion
28 Another Model of the Assembly Map
29 Another Model of the Assembly Map II
30 The Whitehead Space
31 The Whitehead Space II
32 A PullBack Square
33 Digression: Microbundles
34 Overview of Part 3
35 The Setup
36 Combinatorics I
37 Combinatorics II
38 Thickenings of a Point