Reading List
Here are some books and papers that I found very helpful and particularly well written. Many of them are freely available.
- Algebraic Geometry: Vakil's Notes Foundations of Algebraic Geometry, Harris Algebraic Geometry, Eisenbud & Harris The Geometry of Schemes, Shafarevich Basic Algebraic Geometry 1
- Homological algebra: Kashiwara & Schapira Sheaves on Manifolds Chapter 1, Hilton & Stammbach A Course in Homological Algebra
- General Algebraic Topology: Bott & Tu Differential Forms in Algebraic Topology, Aguilar, Gitler & Prieto: Algebraic Topology from a Homotopical Viewpoint, Davis & Kirk Lecture Notes in Algebraic Topology, May A Concise Course in Algebraic Topology
- Cobordism Theory: Stong Notes on Cobordism Theory
- Smooth Manifolds: Lee Introduction to Smooth Manifolds, Morita Geometry of Differential Forms
- Characteristic Classes: Milnor & Stasheff Characteristic Classes, Hatcher Vector Bundles and K-Theory
- Riemann Surfaces: Miranda Algebraic Curves and Riemann Surfaces, Forster Lectures on Riemann Surfaces
- Complex Geometry: Huybrechts Complex Geometry
- Cyclic and Hochschild (Co)homology: Kassel Homology and cohomology of associative algebras
- Lie & Algebraic Groups: Bump Lie Groups, Tauvel & Yu Lie Algebras and Algebraic Groups, Bröcker & tom Dieck Representations of Compact Lie Groups
- Chern-Weil Theory: Dupont Fibre Bundles and Chern-Weil Theory, Morita Geometry of Differential Forms
- Cohomology Operations: Mosher, Tangora Cohomology Operations and Applications in Homotopy Theory
- Derived Categories: Caldararu Derived Categories of Sheaves, Noohi Lectures on derived and triangulated categories
- Stacks: Fantechi Stacks for Everybody, Metzler Topological and Smooth Stacks, Moerdijk Introduction to the language of stacks and gerbes
- Moduli spaces (e.g. stable curves): Kock & Vainsencher An Invitation to Quantum Cohomology
- Simplicial Sets: Riehl A Leisurely Introduction to Simplicial Sets
- Simplicial Homotopy Theory and Model Categories: Dwyer & Spalinski Homotopy theories and model categories, Goerss & Jardine Simplicial Homotopy Theory
- K-Theory: Weibel The K-Book (algebraic K-Theory), Hatcher Vector Bundles and K-Theory (topological K-Theory), Rosenberg Algebraic K-Theory and Its Applications
- Surgery Theory: Ranicki Algebraic and Geometric Surgery
- Simple-Homotopy Theory: Milnor Whitehead Torsion
- Infinite Loop Spaces, Spectra, and Cohomology Theories: Adams Infinite Loop Spaces, Adams Stable Homotopy and Generalized Homology
- PL Manifolds and Kirby-Siebenmann Theory: Rudyak Piecewise Linear Structures on Topological Manifolds
- Galatius-Madsen-Weiss Theory: Hatcher A short exposition of the Madsen-Weiss theorem
- Stable homology: Church Stable homology through scanning