Homology operations for H∞ and Hn ring spectra

1986 ◽  
pp. 56-87 ◽  
Author(s):  
Mark Steinberger
Keyword(s):  
Ring Spectra ◽  
Homology Operations

scholarly journals Homology Operations and Power Series

1985 ◽  
Vol 26 (1) ◽  
pp. 105-105
Author(s):  
Richard Steiner
Keyword(s):  
Power Series ◽  
Ring Spectra ◽  
Homology Operations

Peter May kindly tells me that the proof of the Nishida relations in §8 of this paper works only for E∞ spaces, not for H∞ ring spectra. The reason is that there is no suitable “diagonal” map d for H∞ ring spectra. The result is correct all the same (it is not mine), and its formulation in §3 is also correct.

scholarly journals Homology operations and power series

1983 ◽  
Vol 24 (2) ◽  
pp. 161-168
Author(s):  
Richard Steiner
Keyword(s):  
Power Series ◽  
Loop Spaces ◽  
Similar Treatment ◽  
Ring Spectra ◽  
Homology Operations ◽  
Infinite Loop Spaces ◽  
Infinite Loop ◽  
Cohomology Operations ◽  
Adem Relations

Bullett and Macdonald [1] have used power series to simplify the statement and proof of the Adem relations for Steenrod cohomology operations. In this paper I give a similar treatment of May's generalized Adem relations [4, §4] and of the Nishida relations ([6], [2, 1.1.1(9)], [5, 3.1(7)]). Both sets of relations apply to Dyer-Lashof operations in E∞, spaces such as infinite loop spaces ([3], [2, I.I]) and in H^ ring spectra ([5, §3]).

scholarly journals Ring spectra which are Thom complexes

1979 ◽  
Vol 46 (3) ◽  
pp. 549-559 ◽  
Author(s):  
Mark Mahowald
Keyword(s):  
Ring Spectra

scholarly journals Towards an understanding of ramified extensions of structured ring spectra

2018 ◽  
Vol 168 (3) ◽  
pp. 435-454 ◽  
Author(s):  
BJØRN IAN DUNDAS ◽  
AYELET LINDENSTRAUSS ◽  
BIRGIT RICHTER
Keyword(s):  
Hochschild Homology ◽  
Second Order ◽  
Ring Spectra ◽  
Quotient Maps ◽  
Local Complex ◽  
K Theory ◽  
Tame Ramification ◽  
Topological Hochschild Homology

AbstractWe propose topological Hochschild homology as a tool for measuring ramification of maps of structured ring spectra. We determine second order topological Hochschild homology of the p-local integers. For the tamely ramified extension of the map from the connective Adams summand to p-local complex topological K-theory we determine the relative topological Hochschild homology and show that it detects the tame ramification of this extension. We show that the complexification map from connective topological real to complex K-theory shows features of a wildly ramified extension. We also determine relative topological Hochschild homology for some quotient maps with commutative quotients.

Sign in / Sign up

Export Citation Format

Share Document