Author: Robert R. BrunerPublisher: Springer
ISBN: 3540397787
Category : Mathematics
Languages : en
Pages : 396
Book Description
H Ring Spectra and Their Applications
Author: Robert R. BrunerPublisher: Springer
ISBN: 3540397787
Category : Mathematics
Languages : en
Pages : 396
Book Description
Stable Categories and Structured Ring Spectra
Author: Andrew J. BlumbergPublisher: Cambridge University Press
ISBN: 1009123297
Category : Mathematics
Languages : en
Pages : 441
Book Description
A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.
Algebraic and Geometric Topology, Part 2
Author: R. James MilgramPublisher: American Mathematical Soc.
ISBN: 0821814338
Category : Mathematics
Languages : en
Pages : 330
Book Description
Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Homotopy Theory: Tools and Applications
Author: Daniel G. DavisPublisher: American Mathematical Soc.
ISBN: 1470442442
Category : Literary Collections
Languages : en
Pages : 282
Book Description
This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17–21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.
Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups
Author: John RognesPublisher: American Mathematical Soc.
ISBN: 0821840762
Category : Mathematics
Languages : en
Pages : 154
Book Description
The author introduces the notion of a Galois extension of commutative $S$-algebras ($E_\infty$ ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, real and complex topological $K$-theory, Lubin-Tate spectra and cochain $S$-algebras. He establishes the main theorem of Galois theory in this generality. Its proof involves the notions of separable and etale extensions of commutative $S$-algebras, and the Goerss-Hopkins-Miller theory for $E_\infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions. The author extends the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein and the $p$-complete study for $p$-compact groups by T. Bauer, to a general duality theory for stably dualizable groups in the $E$-local stable homotopy category, for any spectrum $E$.
Global Analysis. Studies and Applications III
Author: Yurii G. BorisovichPublisher: Springer
ISBN: 3540458948
Category : Mathematics
Languages : en
Pages : 338
Book Description
Ring Theory
Author: Jose L. BuesoPublisher: Springer
ISBN: 3540392785
Category : Mathematics
Languages : en
Pages : 343
Book Description
The papers in this proceedings volume are selected research papers in different areas of ring theory, including graded rings, differential operator rings, K-theory of noetherian rings, torsion theory, regular rings, cohomology of algebras, local cohomology of noncommutative rings. The book will be important for mathematicians active in research in ring theory.
A User's Guide to Spectral Sequences
Author: John McClearyPublisher: Cambridge University Press
ISBN: 0521567599
Category : Mathematics
Languages : en
Pages : 579
Book Description
Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
Classifying Spaces and Fibrations
Author: J. Peter MayPublisher: American Mathematical Soc.
ISBN: 0821818554
Category : Classifying spaces
Languages : en
Pages : 116
Book Description
The basic theory of fibrations is generalized to a context in which fibres, and maps on fibres, are constrained to lie in any preassigned category of spaces [script capital] F. Then axioms are placed on [script capital] F to allow the development of a theory of associated principal fibrations and, under several choices of additional hypotheses on [script capital] F, a classification theorem is proven for such fibrations.
Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory
Author: Paul Gregory GoerssPublisher: American Mathematical Soc.
ISBN: 0821832859
Category : Mathematics
Languages : en
Pages : 520
Book Description
As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.