Seiberg-Witten and stable homotopy theory

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:

• http://www.maths.ed.ac.uk/~aar/haupt/

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