The Adams Spectral Sequence for Topological Modular Forms
American Mathematical Society (Verlag)
978-1-4704-6958-0 (ISBN)
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 $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations.
Robert R. Bruner, Wayne State University, Detroit, MI, and University of Oslo, Norway. John Rognes, University of Oslo, Norway.
Introduction
The Adams $E_2$-term: Minimal resolutions
The Davis-Mahowald spectral sequence
Ext over $A(2)$
Ext with coefficients
The Adams differentials: The Adams spectral sequence for $tmf$
The Adams spectral sequence for $tmf/2$
The Adams spectral sequence for $tmf//nu$
The Adams spectral sequence for $tmf/v$
The abutment: The homotopy groups of $tmf$
Duality
The Adams spectral sequence for the sphere
Homotopy of some finite cell $tmf$-modules
Odd primes
Calculation of $E_r(tmf)$ for $r=3,4,5$
Calculation of $R_r(tmf/2)$ for $r=3,4,5$
Calculation of $E_r(tmf//nu)$ for $r=3,4$
Calculation of $E_r(tmf/v)$ for $r=3,4,5$
Bibliography
Index
Erscheinungsdatum | 31.03.2022 |
---|---|
Reihe/Serie | Mathematical Surveys and Monographs |
Verlagsort | Providence |
Sprache | englisch |
Gewicht | 633 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 1-4704-6958-8 / 1470469588 |
ISBN-13 | 978-1-4704-6958-0 / 9781470469580 |
Zustand | Neuware |
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