Product Description: Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of persistence theory, including its algebraic, topological, and algorithmic aspects...read more

Product Description: Rose’s teacher gives stars for spelling and neatness and giving the right answer, but Rose can’t manage to do any of those things right. Will she ever get a star from Mrs. Benson?Rose is a distracted and creative soul. She does her best at school, but sometimes her mind wanders, and she answers the wrong question...read more

Product Description: Concise and authoritative, this monograph is geared toward advanced undergraduate and graduate students. The main theorems whose proofs are given here were first formulated by Lefschetz and have since turned out to be of fundamental importance in the topological aspects of algebraic geometry...read more

This text exposes the basic features of cohomology of sheaves and its applications. The general theory of sheaves is very limited and no essential result is obtainable without turn­ ing to particular classes of topological spaces. The most satis­ factory general class is that of locally compact spaces and it is the study of such spaces which occupies the central part of this text. The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called soft sheaves. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in analysis. The basic example of a soft sheaf is the sheaf of smooth functions on ~n or more generally on any smooth manifold. A rather large effort has been made to demon­ strate the relevance of sheaf theory in even the most elementary analysis. This process has been reversed in order to base the fundamental calculations in sheaf theory on elementary analysis.

Product Description: The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains $D$ which occur as open $G(\mathbb{R})$-orbits in the flag varieties for $G=SU(2,1)$ and $Sp(4)$, regarded as classifying spaces for Hodge structures of weight three...read more

Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices. This text traces the development of this theory from Quillen's fundamental calculation. It presents the stability theorems and low-dimensional results of A. Suslin, W. van der Kallen and others are presented. Coverage also examines the Friedlander-Milnor-conjecture concerning the homology of algebraic groups made discrete.

Product Description: From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; […] one is quickly able to find necessary details...read more

This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and illustrates many applications for the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo-Mumford regularity, the Fulton-Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

"…A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong…This is a nicely-written book [that] studies algebraic differential modules in several variables." --Mathematical Reviews (view table of contents)