Algebraic topology

This volume deals with the theory of finite topological spaces and itsrelationship with the homotopy and simple homotopy theory of polyhedra.

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics withinthe field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

Intersection cohomology assigns groups which satisfy a generalized form of Poincare duality over the rationals to a stratified singular space.

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Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks.

A self-contained introduction is given to J.

Since the injective envelope and projective cover were defined by Eckmann and Bas in the 1960s, they have had great influence on the development of homological algebra, ring theory and module theory.

This book provides a definition of Green functors for a finite group G, and of modules over it, in terms of the category of finite G-sets.

The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity.

This survey covers groups of homotopy self-equivalence classes of topological spaces, and the homotopy type of spaces of homotopy self-equivalences.

The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry.

This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory.

The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes.

Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties.

The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface.

This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras.

In this monograph we give an exposition of some recent development in homotopy theory.

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology.

This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation.

In my long professional life as a mathematician I have had to deliver various survey lectures.

Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa- tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang- Mills connections.

Compactness is related to a number of fundamental concepts of mathemat- ics.

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R.

A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology.

This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002.

This book introduces the category of Cartesian cubical sets and endows it with a Quillen model structure using ideas coming from Homotopy type theory.

This book introduces the category of Cartesian cubical sets and endows it with a Quillen model structure using ideas coming from Homotopy type theory.

This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto.

The theme of this symposium was operator algebras in a wide sense.

The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.

This book constitutes the proceedings of the 4th International Workshop on Computational Topology in Image Context, CTIC 2012, held in Bertinoro, Italy, in May 2012.

Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context.

The key geometric objects underlying Morse homology are the moduli spaces of connecting gradient trajectories between critical points of a Morse function.

This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the "e;Higher homotopical structures"e; programme.

This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the "e;Higher homotopical structures"e; programme.

This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical areas.

The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds.

The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds.

This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects.

This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds.

This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds.

This monograph provides a comprehensive treatment of the classification of small fusion systems, that is, fusion systems with few essential subgroups.