AN INTRODUCTION TO ALGEBRAIC K-THEORY

These are the notes of an introductory lecture given at The 20th Winter School for Geometry and Physics, at Srni. It was meant as a leisurely exposition of classical aspects of algebraic K-theory, with some of its applications to geometry and

[1]  Daniel R. Grayson SK1 of an interesting principal ideal domain , 1981 .

[2]  J. Whitehead,et al.  Simple Homotopy Types , 1950 .

[3]  M. Kervaire Le théorème de Barden-Mazur-Stallings , 1967 .

[4]  D. Quillen On the Cohomology and K-Theory of the General Linear Groups Over a Finite Field , 1972 .

[5]  Kiyoshi Igusa The stability theorem for smooth pseudoisotopies , 1988 .

[6]  R. Oliver Whitehead groups of finite groups , 1988 .

[7]  George A. Elliott,et al.  K-theory , 1999 .

[8]  M. Taylor INTRODUCTION TO CYCLOTOMIC FIELDS(Graduate Texts in Mathematics, 83) , 1983 .

[9]  R. Ho Algebraic Topology , 2022 .

[10]  Hyman Bass,et al.  Algebraic K-theory , 1968 .

[11]  Alan Weinstein,et al.  Progress in mathematics , 1979 .

[12]  J. Rosenberg,et al.  Algebraic K-Theory and Its Applications , 1995 .

[13]  J. Wagoner,et al.  Pseudo-isotopies of compact manifolds , 1973 .

[14]  L. Washington Introduction to Cyclotomic Fields , 1982 .

[15]  C. Weibel,et al.  TWO-PRIMARY ALGEBRAIC K-THEORY OF RINGS OF INTEGERS IN NUMBER FIELDS , 1999 .

[16]  Friedhelm Waldhausen,et al.  ALGEBRAIC K-THEORY OF SPACES I , 1978 .

[17]  John Milnor,et al.  Introduction to algebraic K-theory , 1971 .

[18]  S. A. Mitchell On the Lichtenbaum-Quillen Conjectures from a Stable Homotopy-Theoretic Viewpoint , 1994 .

[19]  A. Borel Stable real cohomology of arithmetic groups , 1974 .

[20]  F. Waldhausen Algebraic K-theory of topological spaces. II , 1979 .

[21]  J. Adams,et al.  Infinite Loop Spaces , 1978 .

[22]  Charles Terence Clegg Wall,et al.  Finiteness conditions for CW complexes. Il , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  Kiyoshi Igusa What happens to Hatcher and Wagoner's formula for πo C(M) when the first Postnikov invariant of M is nontrivial? , 1984 .

[24]  J. Rognes Two-primary algebraic K-theory of pointed spaces , 2002 .

[25]  Ib Madsen,et al.  Algebraic K-theory and traces , 1995 .

[26]  V. Voevodsky The Milnor Conjecture , 1996 .

[27]  C. Wall Finiteness conditions for CW-complex I , 1965 .

[28]  D. Quillen,et al.  Higher algebraic K-theory: I , 1973 .