Categorical Framework For The Study Of Singular Spaces PDF Download
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| Author | : William Fulton |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 174 |
| Release | : 1981 |
| Genre | : Categories |
| ISBN | : 0821822438 |
Download Categorical Framework for the Study of Singular Spaces Book in PDF, ePub and Kindle
In several areas of geometry and topology it has become apparent that the traditional covariant and contravariant functors are insufficient, particularly for dealing with geometric questions about singular spaces. We develop here a new formalism called bivariant theories. These are simultaneous generalizations of covariant group valued "homology-like" theories and contravariant ring valued "cohomology-like" theories. Most traditional pairs of covariant and contravariant theories turn out to extend to bivariant theories. A bivariant theory assigns a group not to an object but to a morphism of the original category; it has products compatible with composition of morphisms. We will also define transformations from one bivariant theory to another, called Grothendieck transformations, which generalize ordinary natural transformations. A number of standard natural transformations turn out to extend to Grothendieck transformations, and this extension has deep consequences.
| Author | : Jörg Schürmann |
| Publisher | : Birkhäuser |
| Total Pages | : 461 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034880618 |
Download Topology of Singular Spaces and Constructible Sheaves Book in PDF, ePub and Kindle
This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.
| Author | : Greg Friedman |
| Publisher | : Cambridge University Press |
| Total Pages | : 491 |
| Release | : 2011-03-28 |
| Genre | : Mathematics |
| ISBN | : 052119167X |
Download Topology of Stratified Spaces Book in PDF, ePub and Kindle
This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
| Author | : Carl-Friedrich Bödigheimer |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : 0821851675 |
Download Mapping Class Groups and Moduli Spaces of Riemann Surfaces Book in PDF, ePub and Kindle
The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of G\"ottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.
| Author | : Armand Borel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 243 |
| Release | : 2009-05-21 |
| Genre | : Mathematics |
| ISBN | : 0817647651 |
Download Intersection Cohomology Book in PDF, ePub and Kindle
This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). Some familiarity with algebraic topology and sheaf theory is assumed.
| Author | : Greg Friedman |
| Publisher | : Cambridge University Press |
| Total Pages | : 824 |
| Release | : 2020-09-24 |
| Genre | : Mathematics |
| ISBN | : 1108895360 |
Download Singular Intersection Homology Book in PDF, ePub and Kindle
Intersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference.
| Author | : David Mumford |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 834 |
| Release | : 2004-07-15 |
| Genre | : Mathematics |
| ISBN | : 9780387210926 |
Download Selected Papers Book in PDF, ePub and Kindle
Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics. Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.
| Author | : Jacques Hurtubise and Eyal Markman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 268 |
| Release | : |
| Genre | : Algebra, Abstract |
| ISBN | : 9780821870334 |
Download Algebraic Structures and Moduli Spaces Book in PDF, ePub and Kindle
This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R 4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.
| Author | : Michael Artin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 485 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1475792867 |
Download Arithmetic and Geometry Book in PDF, ePub and Kindle
| Author | : Piotr Pragacz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 321 |
| Release | : 2006-03-30 |
| Genre | : Mathematics |
| ISBN | : 3764373423 |
Download Topics in Cohomological Studies of Algebraic Varieties Book in PDF, ePub and Kindle
The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis
