skip to content
Algebraic K-Theory and Its Applications Preview this item
ClosePreview this item
Checking...

Algebraic K-Theory and Its Applications

Author: Jonathan Rosenberg
Publisher: New York, NY : Springer New York, 1994.
Series: Graduate texts in mathematics, 147.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jonathan Rosenberg
ISBN: 1461243149 9781461243144
OCLC Number: 1058064119
Language Note: English.
Description: 1 online resource (x, 394 pages).
Contents: 1. K0 of Rings --
1. Defining K0 --
2. K0 from idempotents --
3. K0 of PIDs and local rings --
4. K0 of Dedekind domains --
5. Relative K0 and excision --
6. An application: Swan's Theorem and topological K- theory --
7. Another application: Euler characteristics and the Wall finiteness obstruction --
2.K1 of Rings --
1. Defining K1 --
2. K1 of division rings and local rings --
3. 1 of PIDs and Dedekind domains --
4. Whitehead groups and Whitehead torsion --
5. Relative K1 and the exact sequence --
3. K0 and K1 of Categories, Negative K-Theory --
1. K0 and K1 of categories, Go and G1 of rings --
2. The Grothendieck and Bass-Heller-Swan Theorems --
3. Negative K-theory --
4. Milnor's K2 --
1. Universal central extensions and H2 --
2. The Steinberg group --
3. Milnor's K2 --
4. Applications of K2 --
5. The +?Construction and Quillen K-Theory --
1. An introduction to classifying spaces --
2. Quillen's +?construction and its basic properties --
3. A survey of higher K-theory --
6. Cyclic homology and its relation to K-Theory --
1. Basics of cyclic homology --
2. The Chern character --
3. Some applications --
References --
Books and Monographs on Related Areas of Algebra, Analysis, Number Theory, and Topology --
Books and Monographs on Algebraic K-Theory --
Specialized References --
Notational Index.
Series Title: Graduate texts in mathematics, 147.
Other Titles: Graduate Texts in Mathematics, vol. 147
Responsibility: by Jonathan Rosenberg.

Abstract:

Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Related Subjects:(3)

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/1058064119> # Algebraic K-Theory and Its Applications
    a schema:MediaObject, schema:CreativeWork, schema:Book ;
    library:oclcnum "1058064119" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/32235217#Topic/mathematics> ; # Mathematics
    schema:about <http://dewey.info/class/512.66/e23/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/32235217#Topic/k_theory> ; # K-Theory
    schema:alternateName "Graduate Texts in Mathematics, vol. 147" ;
    schema:author <http://experiment.worldcat.org/entity/work/data/32235217#Person/rosenberg_jonathan> ; # Jonathan Rosenberg
    schema:bookFormat schema:EBook ;
    schema:datePublished "1994" ;
    schema:description "1. K0 of Rings -- 1. Defining K0 -- 2. K0 from idempotents -- 3. K0 of PIDs and local rings -- 4. K0 of Dedekind domains -- 5. Relative K0 and excision -- 6. An application: Swan's Theorem and topological K- theory -- 7. Another application: Euler characteristics and the Wall finiteness obstruction -- 2.K1 of Rings -- 1. Defining K1 -- 2. K1 of division rings and local rings -- 3. 1 of PIDs and Dedekind domains -- 4. Whitehead groups and Whitehead torsion -- 5. Relative K1 and the exact sequence -- 3. K0 and K1 of Categories, Negative K-Theory -- 1. K0 and K1 of categories, Go and G1 of rings -- 2. The Grothendieck and Bass-Heller-Swan Theorems -- 3. Negative K-theory -- 4. Milnor's K2 -- 1. Universal central extensions and H2 -- 2. The Steinberg group -- 3. Milnor's K2 -- 4. Applications of K2 -- 5. The +?Construction and Quillen K-Theory -- 1. An introduction to classifying spaces -- 2. Quillen's +?construction and its basic properties -- 3. A survey of higher K-theory -- 6. Cyclic homology and its relation to K-Theory -- 1. Basics of cyclic homology -- 2. The Chern character -- 3. Some applications -- References -- Books and Monographs on Related Areas of Algebra, Analysis, Number Theory, and Topology -- Books and Monographs on Algebraic K-Theory -- Specialized References -- Notational Index."@en ;
    schema:description "Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/32235217> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://worldcat.org/issn/0072-5285> ; # Graduate texts in mathematics ;
    schema:isSimilarTo <http://worldcat.org/entity/work/data/32235217#CreativeWork/> ;
    schema:name "Algebraic K-Theory and Its Applications"@en ;
    schema:productID "1058064119" ;
    schema:url <http://dx.doi.org/10.1007/978-1-4612-4314-4> ;
    schema:url <http://proxy.lib.utk.edu:90/login?url=http://dx.doi.org/10.1007/978-1-4612-4314-4> ;
    schema:url <https://ezproxy.aub.edu.lb/login?url=https://doi.org/10.1007/978-1-4612-4314-4> ;
    schema:workExample <http://dx.doi.org/10.1007/978-1-4612-4314-4> ;
    schema:workExample <http://worldcat.org/isbn/9781461243144> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/1058064119> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/32235217#Person/rosenberg_jonathan> # Jonathan Rosenberg
    a schema:Person ;
    schema:familyName "Rosenberg" ;
    schema:givenName "Jonathan" ;
    schema:name "Jonathan Rosenberg" ;
    .

<http://experiment.worldcat.org/entity/work/data/32235217#Topic/k_theory> # K-Theory
    a schema:Intangible ;
    schema:name "K-Theory"@en ;
    schema:name "K-theory"@en ;
    .

<http://worldcat.org/isbn/9781461243144>
    a schema:ProductModel ;
    schema:isbn "1461243149" ;
    schema:isbn "9781461243144" ;
    .

<http://worldcat.org/issn/0072-5285> # Graduate texts in mathematics ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/1058064119> ; # Algebraic K-Theory and Its Applications
    schema:issn "0072-5285" ;
    schema:name "Graduate texts in mathematics ;" ;
    schema:name "Graduate Texts in Mathematics," ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.