Overviews
- Lectures on the triangulation conjecture - Manolescu
- The Conley Index, gauge theory and triangulations - Manolescu
- Three lectures on the stable homotopy type of Seiberg-Witten Floer homology - Behrens
Principal bundles, spin geometry and Index Theory
- Fibre Bundles - Husemoller
- Spin geometry - Lawson and Michelsohn
- Elliptic operators, topology and asymptotic methods - Roe
- The Atiyah-Singer index theorem: what it is and why you should care - Mazzeo
- Lectures on Dirac operators and Index Theory - Dai
- Geometry of Dirac operators - Freed
Seiberg-Witten Theory
- The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds - Morgan
- Seiberg-Witten Gauge Theory - Marcolli
Morse Theory and Floer Theory
- Topology from the differentiable viewpoint - Milnor
- Morse Theory - Milnor
- An Invitation to Morse Theory - Nicolaescu
Stable homotopy theory and equivariant cohomology
- A concise course in algebraic topology - May
- Infinite loop spaces - Adams
- Equivariant stable homotopy theory - Lewis, May and Steinberger
Stable homotopy invariants for the 4-dimensional Seiberg-Witten equations
- A stable cohomotopy refinement of Seiberg-Witten invariants: I - Bauer and Furuta
- A stable cohomotopy refinement of Seiberg-Witten invariants: II - Bauer
- Refined Seiberg-Witten invariants - Bauer
- Finite dimensional approximations in geometry - Furuta
- Homology cobordism group of homology 3-spheres - Furuta
- Monopole equation and the 11/8-conjecture - Furuta
- Homotopy theoretical considerations of the Bauer-Furuta stable homotopy Seiberg-Witten invariants - Furuta, Kametani, Matsue and Minami
- The fibrewise Leray-Schauder index - Crabb
Conley Index Theory
- The Conley Index Theory: A brief introduction - Mischaikow
- Lecture notes on Morse and Conley Theory - Weber
Stable homotopy types for Seiberg-Witten Floer homology
- Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture - Manolescu
- The equivalence of two Seiberg-Witten Floer homologies - Lidman and Manolescu
- Twisted Manolescu-Floer spectra for Seiberg-Witten monopoles - Tirasan Khandhawit
- A new gauge slice for the relative Bauer-Furuta invariants - Tirasan Khandhawit
Triangulation conjecture and Hauptvermutung
- Foundational Essays on Topological Manifolds, Smoothings, and Triangulations - Kirby and Siebenmann
- Simplicial triangulations of topological manifolds - Galewski and Stern
- Classification of simplicial triangulations of topological manifolds - Galewski and Stern
- The triangulation of manifolds (overview) - Quinn
And check out the many links on the following website:
Other stable homotopy types in low-dimensional topology
- The homotopy theory of Khovanov homology - Everitt and Turner
- A Khovanov homotopy type - Lipshitz and Sarkar
- Khovanov homotopy type, Burnside category, and products - Lawson, Lipshitz and Sarkar
- Field theories, stable homotopy theory and Khovanov homology - Hu, Kriz and Kriz
- Derived Representation Theory and Stable Homotopy Categorification of sl_k - Hu, Kriz and Somberg
- An sl_n stable homotopy type for matched diagrams - Jones, Lobb and Schuetz
- A Khovanov stable homotopy type for colored links - Lobb, Orson and Schuetz