Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial

Cover
Title page
Contents
Preface
V. A. Rokhlin (23 August 1919–3 December 1984), materials for the biography
	Bibliography of V. A. Rokhlin
	About V. A. Rokhlin
Teaching mathematics to non-mathematicians
	Notes by Oleg Viro
Vladimir Abramovich Rokhlin and algebraic topology
	1. Introduction
	2. Bordism groups
	3. The signature and its applications
	4. The signature of 4-dimensional manifolds
	5. Framed bordism, and the Rokhlin and Milnor–Kervaire theorems
	6. Thom spaces and Atiyah duality
	7. The theories of complex bordism ?_{*}(?) and cobordism ?*(?)
	8. The loop space of ?³ and the coefficients of the Chen–Dold character
	9. The signature of partially framed manifolds
	References
Amenability of groupoids and asymptotic invariance of convolution powers
	Introduction
	1. Amenable groupoids
	2. Markov chains on groupoids and approximate invariance
	3. Amenable actions
	References
Slopes of links and signature formulas
	1. Introduction
	2. The signature formula
	3. The slope
	4. Slopes via ?-complexes
	5. Concordance invariance
	References
?-rigidity of the property to be an almost Pogorelov polytope
	Introduction
	1. Cohomology ring of a moment-angle manifold of a simple 3-polytope
	2. ?-rigidity of Pogorelov polytopes
	3. Cohomological rigidity of the property to be an almost Pogorelov polytope
	4. Generalization of the technique to almost Pogorelov polytopes
	5. Remark
	Acknowledgments
	References
The first homology of a real cubic is generated by lines
	1. Introduction
	2. The case of nodal cubics
	3. Passing to nonsingular cubics
	4. Concluding remarks
	Acknowledgments
	References
Circular orders, ultra-homogeneous order structures, and their automorphism groups
	1. Introduction
	2. Some generalizations of (extreme) amenability
	3. Circular order, topology, and inverse limits
	4. Ultrahomogeneous actions on circularly ordered sets
	5. The Fraïssé class of finite circularly ordered systems and the KPT theory
	6. Automatic continuity and Roelcke precompactness
	7. Some perspectives and questions
	8. Appendix: Large ultrahomogeneous circularly ordered sets
	Acknowledgments
	References
Convergence of equilibrium measures corresponding to finite subgraphs of infinite graphs: New examples
	1. Introduction
	2. Preliminary information and statement of the problem
	3. Linear graphs
	4. Existence of an irregular sequence
	5. Existence of a regular sequence
	6. Concluding remarks
	References
Anti-symplectic involutions on rational symplectic 4-manifolds
	1. Introduction
	2. Tools
	3. Proof outline
	References
Dolbeault cohomology of complex manifolds with torus action
	1. Introduction
	2. Preliminaries: holomorphic foliations on complex manifolds
	3. Fujiki foliations
	4. Basic Dolbeault cohomology of the canonical foliations on complex moment-angle manifolds
	5. Manifolds with maximal torus actions
	6. Dolbeault cohomology of moment-angle manifolds
	Acknowledgment
	References
Poincaré polynomials of generic torus orbit closures in Schubert varieties
	1. Introduction
	2. Backgrounds: Polytopes and projective toric varieties
	3. Generic torus orbit closures in Schubert varieties and their Poincaré polynomials
	4. Proof of Theorem 3.6
	5. Concluding remarks
	Acknowledgment
	References
Higher order Massey products and applications
	Introduction
	1. Massey products in cohomology
	2. Massey products and Lie algebras representations
	3. ?-step Massey products in Lie algebra cohomology
	4. Non-trivial Massey products in Lie algebra cohomology
	5. Massey products in Koszul homology of local rings
	6. Massey products in Toric Topology and nonformality of polyhedral products
	Acknowledgments
	References
Discreteness of deformations of cocompact discrete subgroups
	1. Introduction
	2. Preliminaries
	3. Deformations and discreteness
	Acknowledgments
	References
Topological isotopy and Cochran’s derived invariants
	1. Introduction
	2. Invariants
	3. Realization
	4. Rationality
	Acknowledgment
	References
Geometric description of the Hochschild cohomology of group algebras
	1. Introduction
	2. The smooth version of Johnson’s problem
	3. Hochschild (co)homology
	4. Hochschild homology
	5. Conclusion
	6. Addendum: Comparison of homology and cohomology
	References
A user’s guide to basic knot and link theory
	1. Main definitions and results on knots
	2. Main definitions and results on links
	3. Some basic tools
	4. The Gauss linking number modulo 2 via plane diagrams
	5. The Arf invariant
	6. Appendix: Proper colorings
	7. Oriented knots and links and their connected sums
	8. The Gauss linking number via plane diagrams
	9. The Casson invariant
	10. Alexander-Conway polynomial
	11. Vassiliev-Goussarov invariants
	12. Appendix: Some details
	Acknowledgments
	References
Group actions: Entropy, mixing, spectra, and generic properties
	1. Basic definitions
	2. ?-actions and spectra of boundary value problems
	3. Entropy
	4. Generic properties: Definition
	5. Approximation of group actions
	6. Cardinal-valued invariants of measure-preserving transformations
	7. Spectral problems
	8. Rokhlin’s multiple mixing problem
	9. Linear extensions of dynamical systems: The spectral theory and MET
	References
Rokhlin’s theorem, a problem and a conjecture
Maximally inflected real trigonal curves on Hirzebruch surfaces
	1. Introduction
	2. Trigonal curves and elliptic surfaces
	3. Dessins
	4. Skeletons
	5. A constructive description of maximally inflected trigonal curves
	6. Rigid isotopies and week equivalence
	Acknowledgment
	References
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