前辅文
 Chapter 1. Geometry and Combinatorics of Polytopes
  1.1. Convex polytopes
  1.2. Gale duality and Gale diagrams
  1.3. Face vectors and Dehn–Sommerville relations
  1.4. Characterising the face vectors of polytopes
  Polytopes: Additional Topics
  1.5. Nestohedra and graph-associahedra
  1.6. Flagtopes and truncated cubes
  1.7. Differential algebra of combinatorial polytopes
  1.8. Families of polytopes and differential equations
 Chapter 2. Combinatorial Structures
  2.1. Polyhedral fans
  2.2. Simplicial complexes
  2.3. Barycentric subdivision and flag complexes
  2.4. Alexander duality
  2.5. Classes of triangulated spheres
  2.6. Triangulated manifolds
  2.7. Stellar subdivisions and bistellar moves
  2.8. Simplicial posets and simplicial cell complexes
  2.9. Cubical complexes
 Chapter 3. Combinatorial Algebra of Face Rings
  3.1. Face rings of simplicial complexes
  3.2. Tor-algebras and Betti numbers
  3.3. Cohen–Macaulay complexes
  3.4. Gorenstein complexes and Dehn–Sommerville relations
  3.5. Face rings of simplicial posets
  Face Rings: Additional Topics
  3.6. Cohen–Macaulay simplicial posets
  3.7. Gorenstein simplicial posets
  3.8. Generalised Dehn–Sommerville relations
 Chapter 4. Moment-Angle Complexes
  4.1. Basic definitions
  4.2. Polyhedral products
  4.3. Homotopical properties
  4.4. Cell decomposition
  4.5. Cohomology ring
  4.6. Bigraded Betti numbers
  4.7. Coordinate subspace arrangements
  Moment-Angle Complexes: Additional Topics
  4.8. Free and almost free torus actions on moment-angle complexes
  4.9. Massey products in the cohomology of moment-angle complexes
  4.10. Moment-angle complexes from simplicial posets
 Chapter 5. Toric Varieties and Manifolds
  5.1. Classical construction from rational fans
  5.2. Projective toric varieties and polytopes
  5.3. Cohomology of toric manifolds
  5.4. Algebraic quotient construction
  5.5. Hamiltonian actions and symplectic reduction
 Chapter 6. Geometric Structures on Moment-Angle Manifolds
  6.1. Intersections of quadrics
  6.2. Moment-angle manifolds from polytopes
  6.3. Symplectic reduction and moment maps revisited
  6.4. Complex structures on intersections of quadrics
  6.5. Moment-angle manifolds from simplicial fans
  6.6. Complex structures on moment-angle manifolds
  6.7. Holomorphic principal bundles and Dolbeault cohomology
  6.8. Hamiltonian-minimal Lagrangian submanifolds
 Chapter 7. Half-Dimensional Torus Actions
  7.1. Locally standard actions and manifolds with corners
  7.2. Toric manifolds and their quotients
  7.3. Quasitoric manifolds
  7.4. Locally standard T-manifolds and torus manifolds
  7.5. Topological toric manifolds
  7.6. Relationship between different classes of T-manifolds
  7.7. Bounded flag manifolds
  7.8. Bott towers
  7.9. Weight graphs
 Chapter 8. Homotopy Theory of Polyhedral Products
  8.1. Rational homotopy theory of polyhedral products
  8.2. Wedges of spheres and connected sums of sphere products
  8.3. Stable decompositions of polyhedral products
  8.4. Loop spaces, Whitehead and Samelson products
  8.5. The case of flag complexes
 Chapter 9. Torus Actions and Complex Cobordism
  9.1. Toric and quasitoric representatives in complex bordism classes
  9.2. The universal toric genus
  9.3. Equivariant genera, rigidity and fibre multiplicativity
  9.4. Isolated fixed points: localisation formulae
  9.5. Quasitoric manifolds and genera
  9.6. Genera for homogeneous spaces of compact Lie groups
  9.7. Rigid genera and functional equations
 Appendix A. Commutative and Homological Algebra
  A.1. Algebras and modules
  A.2. Homological theory of graded rings and modules
  A.3. Regular sequences and Cohen–Macaulay algebras
  A.4. Formality and Massey products
 Appendix B. Algebraic Topology
  B.1. Homotopy and homology
  B.2. Elements of rational homotopy theory
  B.3. Eilenberg–Moore spectral sequences
  B.4. Group actions and equivariant topology
  B.5. Stably complex structures
  B.6. Weights and signs of torus actions
 Appendix C. Categorical Constructions
  C.1. Diagrams and model categories
  C.2. Algebraic model categories
  C.3. Homotopy limits and colimits
 Appendix D. Bordism and Cobordism
  D.1. Bordism of manifolds
  D.2. Thom spaces and cobordism functors
  D.3. Oriented and complex bordism
  D.4. Characteristic classes and numbers
  D.5. Structure results
  D.6. Ring generators
 Appendix E. Formal Group Laws and Hirzebruch Genera
  E.1. Elements of the theory of formal group laws
  E.2. Formal group law of geometric cobordisms
  E.3. Hirzebruch genera (complex case)
  E.4. Hirzebruch genera (oriented case)
  E.5. Krichever genus
 Bibliography
 Index