Characteristic Classes of Singular Varieties -- Lectures on the Geometry of Flag Varieties -- Combinatorial K-theory -- Morse Functions and Cohomology of Homogeneous Spaces -- Integrable Systems and Gromov-Witten Theory -- Multiplying Schubert Classes -- Lectures on Characteristic Classes of Constructible Functions -- Algebraic K-theory of Schemes -- Gromov-Witten Invariants and Quantum Cohomol…
Preface -- Introduction -- Set Theory -- Metric Spaces -- Set Theoretic Topology -- Systems of Continuous Functions -- Basic Algebraic Topology -- The Classical Mittag-Leffler Theorem Derived from Bourbaki’s -- Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces -- The Arzela-Ascoli Theorem -- References -- List of Symbols -- Index.If mathematics is a language, then taking a top…
A Motivating Problem -- to the Novikov and the Borel Conjecture -- Normal Bordism Groups -- The Signature -- The Signature Theorem and the Novikov Conjecture -- The Projective Class Group and the Whitehead Group -- Whitehead Torsion -- The Statement and Consequences of the s-Cobordism Theorem -- Sketch of the Proof of the s-Cobordism Theorem -- From the Novikov Conjecture to Surgery -- Surgery …
Plane Algebraic Curves -- Ane Algebraic Curves -- Projective Algebraic Curves -- The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves -- Rational Functions on Algebraic Curves -- Intersection Multiplicity and Intersection Cycle of Two Curves -- Regular and Singular Points of Algebraic Curves. Tangents -- More on Intersection Theory. Applications -- Rational Maps. Parame…
Parafree Groups -- The Finitary Andrews-Curtis Conjecture -- Cuts in Kähler Groups -- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries -- Solved and Unsolved Problems Around One Group -- Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators -- Survey on Classifying Spaces for Families of Subgroups -- Are Unitarizable Groups Amenable? -- Probabil…
Homological Methods in Fixed Point Theory -- Coincidence Theory -- On the Lefschetz Fixed Point Theorem -- Linearizations for Maps of Nilmanifolds and Solvmanifolds -- Homotopy Minimal Periods -- Periodic Points and Braid Theory -- Fixed Point Theory of Multivalued Weighted Maps -- Fixed Point Theory for Homogeneous Spaces A Brief Survey -- Equivariant Fixed Point Theory -- A Note on Equivarian…
Part I: Foundations and Computations: Deloopings in Algebraic K- theory -- The Motivic Spectral Sequence -- K-theory of truncated polynomial algebras -- Bott Periodicity in Topological, Algebraic and Hermitian K-theory -- Algebraic K-theory of Rings and Integers in Local and Global Fields. Part II: K-theory and Algebraic Geometry: Motivic Cohomology, K-theory and topological cyclic Homology -- …
Curvature of Contact Metric Manifolds -- A Case for Curvature: the Unit Tangent Bundle -- Convex Hypersurfaces in Hadamard Manifolds -- Contact Metric Geometry of the Unit Tangent Sphere Bundle -- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds -- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds -- Commutative Condition on the S…
Noncommutative Geometry -- Poisson Geometry and Deformation Quantization -- Applications in Physics -- Topological Quantum Field Theory.This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challeng…