Technical Books

This book contains below topics, Prerequisites, General properties of the Kgroup of a TPC, Filtered chain complexes, Barcodes step functions and Ktheory for persistence modules, A Ktheoretic pairing, Measurements on the Kgroup and on barcodes, Symplectic Applications.

This note contains below topics, On the TC of formal DGAs with polynomial homology, The May filtration on topological negative cyclic homology and topological periodic cyclic homology, Cardinality of topological cyclic homology, Coefficients in algebraically closed fields, On the algebraic Ktheory of truncated witt vectors, On the algebraic Ktheory of motivic pullback squares, Bockstein spectral sequences and syntomic cohomology, On the K 1 local algebraic Ktheory of K 1.

This book contains below topics, Hochschild homology and motivic filtrations, Filtering the motivic associated graded, Detection, Prismatic cohomology, Syntomic cohomology, Topological cyclic homology and algebraic Ktheory.

This paper considers smooth extensions of cohomology theories. It constructs a multiplicative model of smooth K theory, and a push forward for a proper submersion with a smooth K orientation. It also lifts the Chern character to this smooth setting.

This book contains below topics, Direct Sums, Inner Products, Tensor Product s, Associated Fiber Bundles, Clutching Functions, The Universal Bundle, Cell Structures on Grassmannians, Paracompac tness, The Fundamental Product Theorem, Deducing Periodicity from the Product T heorem, Extending to a Cohomology Theory.

This book consist as a first course in the calculus. In the treatment of each topic, the text is intended to contain a precise statement of the fundamental principle involved, and to insure the students clear understanding of this principle, without districting his attention by the discussion of a multitude of details.

This book describes the following topics, Standard Forms, Change Of The Independent Variable,Integration by parts and powers of Sines and cosines, Rational Algebraic Fractional Forms, Reduction Formulae, General Theorems, Differentiation Of a definite Integral with regard to a parameter, Rectification Of Twisted Curves, Moving Curves, Surfaces and volumes in general.

This book covers the following topics, Fundamental integration formulae, Integration by substitution, Integration by parts, Integration by partial fractions, Definite Integration as the limit of a sum, Properties of definite Integrals, differential equations and Homogeneous differential equations.

This book describes the following topics, Elementary functions and their classification, The integration of elementary functions, The integration of rational functions, The integration of algebraical functions and The integration of transcendental functions.

This book contains below topics, Functions and Graphs, Limits, Derivatives, Applications of Derivatives, Integration, Applications of Integration, Table of Integrals, Table of Derivatives, Review of PreCalculus.

This note contains below topics, Preliminaries, Boolean cumulants of free random variables, Calculus for conditional expectations, Calculus for the block cumulant functional b, Linearization and conditional expectations, Examples, An algebraic approach to Boolean cumulants, Rational series and linearizations.

This note covers universal constructions, Tensor products, Injective, Projective and flat module, Homology, Resolutions, Ext and Tor, Depth, Chain maps and induced maps on Ext and tor, Ext, Tor and homological dimensions, Long exact sequences, Depth and homological dimensions, Regular local rings.

This note contains below topics, Preliminaries and Summary, Semialgebras and Semitensor Product, Derived Functor SemiTor, Semicontramodules and Semihomomorphisms, Derived Functor SemiExt, ComoduleContramodule Correspondence, SemimoduleSemicontramodule Correspondence, Functoriality in the Coring, Functoriality in the Semialgebra, Closed Model Category Structures, A Construction of Semialgebras, Relative Nonhomogeneous Koszul Duality, Contramodules over Coalgebras over Fields, Comparison with Arkhipov s 39 42 5 613A 45 47 2mu 6muplus1mu 603AExt 2 and Sevostyanov s 39 42 5 613A 45 47 2mu 6muplus1mu 603ATor 2, Semialgebras Associated to HarishChandra Pairs, Tate HarishChandra Pairs and Tate Lie Algebras, Groups with Open Profinite Subgroups, Algebraic Groupoids with Closed Subgroupoids.

This note contains below topics, Standard Homological Algebra, Spectral sequences, Effective homology, Constructive Homology and Commutative Algebra, Effective homology of Koszul complexes, Simplicial sets, Serre spectral sequence, The EilenbergMoore spectral sequence, The claimed Postnikov invariants This section is a rough copy of the paper RBSR8 which explains some redundancies and also some gaps with respect to the previous sections in spite of these defects we think a reader having reached this point of the text could be interested by this section making obvious a surrealist error in the standard terminology of Algebraic Topology.

This book contains below topics, The commutative algebra of monoids, Homological algebra, Complexes and computation, Geometry of monoids.