The Mathematical Sciences Research Institute (MSRI), founded in , is an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions. The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to Grizzly Peak, on the. algebraic K-theory, and homotopy theory. Familiarity with these topics is important not just for a topology student but any student of pure mathe-matics, including the student moving towards research in geometry, algebra, or analysis. The prerequisites for a course based on this book include a workingFile Size: 3MB. A First Book in Algebra, by Wallace C. Boyden; Theory of Groups of Finite Order, by William Burnside Algebraic K-Theory and Its Applications,Jonathan Rosenberg. Algebraic Number Theory,Serge : Kevin de Asis. Writings. With Eric Friedlander, An overview over algebraic K-theory, in Algebraic K-theory and its applications, World Scientific , pp. 1– ( Trieste Lecture Notes); Weibel, Charles A. (), The K-book, Graduate Studies in Mathematics, , American Mathematical Society, Providence, RI, ISBN , MR With Carlo Mazza, Vladimir Voevodsky Lectures on Motivic.

When the algebraic K-theory group NK_1(ZG) is nontrivial (e.g., for G=Z/4), we show the dynamical zeta function for any such extension is consistent with infinitely many topological conjugacy classes. A Concise Course in Algebraic Topology (J. P. May) This book explains the following topics: The fundamental group and some of its applications, Categorical language and the van Kampen theorem, Covering spaces, Graphs, Compactly generated spaces, Cofibrations, Fibrations, Based cofiber and fiber sequences, Higher homotopy groups, CW complexes. I have now returned to an earlier plan of having this material be an extra chapter of the Algebraic Topology book, rather than a separate book. The current version of this chapter is here. Its main focus is the Serre spectral sequence and its applications, but there is also some coverage of the Adams spectral sequence and, more briefly, a few. The theme of this book is infinite loop space theory and its multiplicative elaboration. The main goal is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory. ( views) The Homology of Iterated Loop Spaces by F. R. Cohen, T. J. Lada, P. J. May.

Algebraic \(K\)-theory, which is the main character of this book, deals mainly with studying the structure of rings. However, it turns out that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the . On the Farrell-Jones Conjecture and its applications ArthurBartels,WolfgangLu¨ckandHolgerReich Abstract. We present the status of the Farrell-Jones Conjecture for algebraic K-theory for a group Gand arbitrary coeﬃcient rings R. We add new groups for which the conjec-ture is known to be true and study inheritance properties. We discuss new. And is there material (lecture Video or good pdf script) where the algebraic K-theory is explained? Nothing very accessible for algebraic K-theory. Blackadar's book for K-theory of operator algebras, and Atiyah's book for topological K-theory as it stood in the 's, are readable without a lot of algebraic . Then you may have a look at Blackadar's book "K-Theory for Operator Algebras", Lemma If you have the definition by finiteily generated projective modules in mind, have a look at Rosenbergs Book "Algebraic K-Theory and its applications", Lemma $\endgroup$ – Epsilon Apr 14 '19 at