Robert Ray Bruner's Books

Connective Real $K$-Theory of Finite Groups

By: Robert Ray Bruner,John Patrick Campbell Greenlees

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Connective Real $K$-Theory of Finite Groups

By: Robert Ray Bruner,John Patrick Campbell Greenlees

Focusing on the study of real connective $K$-theory including $ko^*(BG)$ as a ring and $ko_*(BG)$ as a module over it, the authors define equivariant versions of connective $KO$-theory and connective $K$-theory with reality, in the sense of Atiyah, which give well-behaved, Noetherian, uncompleted versions of the theory.

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Page Count

328

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851896

ISBN 13

9780821851890

The Connective K-Theory of Finite Groups

By: Robert Ray Bruner,John Patrick Campbell Greenlees

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The Connective K-Theory of Finite Groups

By: Robert Ray Bruner,John Patrick Campbell Greenlees

Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $ku DEGREES*(BG)$ where $ku$ denotes connective complex K-theory. It describes the variety in terms of the category of abelian $p$-subgroups of $G$ for primes $p$ dividing the group

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Page Count

144

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821833669

ISBN 13

9780821833667

The Adams Spectral Sequence for Topological Modular Forms

By: Robert R. Bruner,John Rognes

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The Adams Spectral Sequence for Topological Modular Forms

By: Robert R. Bruner,John Rognes

The connective topological modular forms spectrum, tmf, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of tmf and several tmf-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The H∞ ring structure of the sphere and of tmf are used to determine many differentials and relations.

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Page Count

690

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470456745

ISBN 13

9781470456740

Book's by Robert Ray Bruner

Connective Real $K$-Theory of Finite Groups

Connective Real $K$-Theory of Finite Groups

The Connective K-Theory of Finite Groups

The Connective K-Theory of Finite Groups

The Adams Spectral Sequence for Topological Modular Forms

The Adams Spectral Sequence for Topological Modular Forms

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