Influence of Solomon Lefschetz in Geometry and Topology : 50 Years of Mathematics at CINVESTAV.

Cover -- Title page -- Contents -- Preface -- Solomon Lefschetz and Mexico -- Recent Progress in Symplectic Flexibility -- 1. Flexible vs. Rigid Symplectic Topology -- 2. Flexible milestones after the resolution of Gromov's alternative -- 3. Renaissance of the ℎ-principle in symplectic topology -- References -- Equivariant Extensions of Differential Forms for Non-compact Lie Groups -- 1. Introduction -- 2. Equivariant cohomology -- 3. Equivariant extension of differential forms -- 4. Equivariant extensions of the WZW term for ( ,\real) actions -- References -- From Classical Theta Functions to Topological Quantum Field Theory -- 1. Introduction -- 2. Theta functions -- 3. Theta functions in the abstract setting -- 4. A topological model for theta functions -- 5. The discrete Fourier transform as a skein -- 6. The Egorov identity and handle slides -- 7. The topological quantum field theory associated to theta functions -- 8. The Hermite-Jacobi action and the non-additivity of the signature of 4-dimensional manifolds -- 9. Theta functions and abelian Chern-Simons theory -- References -- Toric Topology -- 1. Introduction -- 2. Polyhedral product spaces -- 3. Cup products in polyhedral products -- 4. Rational homotopy of moment angle complexes -- 5. Geometric realization of monomial ideal rings -- 6. Infinite families of toric manifolds associated to a given one -- 7. Intersection of quadrics, moment angle manifolds, and connected sum -- References -- Beilinson Conjecture for Finite-dimensional Associative Algebras -- Introduction -- 1. Beilinson conjecture -- 2. Kato's reformulation -- 3. Non-commutative version -- References -- Partial Monoids and Dold-Thom Functors -- 1. Introduction -- 2. Partial monoids and infinite loop spaces -- 3. Properties of Dold-Thom functors coming from spectra -- 4. Quasifibrations and Dold-Thom functors.

5. On the spectrum [ ] -- References -- The Weak b-principle -- 1. The h-principle -- 2. The b-principle -- 3. The weak b-principle -- 4. Broken solutions -- 5. The homotopy type of ℎℳ_{ℛ} -- 6. Final remarks -- References -- Orbit Configuration Spaces -- 1. Introduction -- 2. Definition and main properties -- 3. Loop spaces of orbit configuration spaces -- 4. The homology ring _{*}(Ω _{ }(ℝⁿ)) -- 5. The cohomology of _{ }(ℝℙⁿ) -- 6. Braids groups on surfaces -- 7. Non-formality of configuration spaces -- 8. Proof of Theorem 2.2 -- References -- Dynamical Systems and Categories -- 1. Introduction -- 2. Entropy of endofunctors -- 2.1. Complexity in triangulated categories -- 2.2. Entropy of exact endofunctors -- 2.3. The case of saturated _{∞}-categories -- 2.4. Example: semisimple categories -- 2.5. Regular maps -- 2.6. Entropy of the Serre functor -- 2.7. Pseudo-Anosov maps -- 3. Density of phases -- 3.1. Preliminaries -- 3.2. Dynkin, Euclidean quivers and Kronecker quiver -- 3.3. Kronecker pairs -- 3.4. Application to quivers -- 3.5. Further examples of Kronecker pairs -- 4. Open questions -- 4.1. Algebraicity of entropy -- 4.2. Pseudo-Anosov autoequivalences -- 4.3. Birational maps -- 4.4. Dynamical spectrum -- 4.5. Complexity and mass -- 4.6. Questions related to Kronecker pairs and density of phases -- References -- The Nahm Pole Boundary Condition -- 1. Introduction -- 2. Uniqueness Theorem For The Nahm Pole Solution -- 2.1. Solutions On A Four-Manifold Without Boundary -- 2.2. A Weitzenbock Formula Adapted To The Nahm Pole -- 2.3. The Indicial Equation -- 2.4. The Nahm Pole Boundary Condition -- 2.5. The Boundary Terms And The Vanishing Theorem -- 2.6. Behavior At Infinity -- 2.7. Extension To Five Dimensions -- 3. The Linearized Operator On A Half-Space -- 3.1. Overview -- 3.2. Vanishing Theorem For The Kernel -- 3.3. Index.

3.4. Pseudo Skew-Adjointness -- 3.5. Extension To Five Dimensions -- 4. The Nahm Pole Boundary Condition On A Four-Manifold -- 4.1. Boundary Conditions on the Connection -- 4.2. The Index -- 5. Analytic theory -- 5.1. Uniformly Degenerate Operators -- 5.2. Elliptic Weights -- 5.3. Structure of the Generalized Inverse -- 5.4. Algebraic Boundary Conditions and Ellipticity -- 5.5. Regularity of Solutions of the KW Equations -- Appendix A. Some Group Theory -- Acknowledgments -- References -- Back Cover.

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