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9781470468781 Academic Inspection Copy

A Multiplicative Tate Spectral Sequence for Compact Lie Group Actions

  • ISBN-13: 9781470468781
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Alice Hedenlund, By John Rognes
  • Price: AUD $219.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 29/08/2024
  • Format: Paperback (254.00mm X 178.00mm) 134 pages Weight: 118g
  • Categories: Geometry [PBM]Topology [PBP]
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Given a compact Lie group G and a commutative orthogonal ring spectrum R such that R[G]* = ?*(R ? G+) is finitely generated and projective over ?*(R), we construct a multiplicative G-Tate spectral sequence for each R-module X in orthogonal G-spectra, with E2-page given by the Hopf algebra Tate cohomology of R[G]* with coefficients in ?*(X). Under mild hypotheses, such as X being bounded below and the derived page RE? vanishing, this spectral sequence converges strongly to the homotopy ?*(XtG) of the G-Tate construction XtG = [EG ? F(EG+, X]G.
Alice Hedenlund, University of Oslo, Norway. John Rognes, University of Oslo, Norway.
1. Introduction 2. Tate Cohomology for Hopf Algebras 3. Homotopy Groups of Orthogonal $G$-Spectra 4. Sequences of Spectra and Spectral Sequences 5. The $G$-Homotopy Fixed Point Spectral Sequence 6. The $G$-Tate Spectral Sequence
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