scholarly journals The plus-construction, Bousfield localization, and derived completion

2010 ◽  
Vol 214 (5) ◽  
pp. 596-604 ◽  
Author(s):  
Tyler Lawson
Keyword(s):  
Plus Construction ◽  
Bousfield Localization

scholarly journals A controlled plus construction for crumpled laminations

1994 ◽  
Vol 342 (2) ◽  
pp. 807-826
Author(s):  
R. J. Daverman ◽  
F. C. Tinsley
Keyword(s):  
Plus Construction

On the quotients of mapping class groups of surfaces by the Johnson subgroups

2019 ◽  
pp. 1-23
Author(s):  
TOMÁŠ ZEMAN
Keyword(s):  
Boundary Component ◽  
Loop Space ◽  
Mapping Class Groups ◽  
Mapping Class ◽  
Classifying Spaces ◽  
Class Groups ◽  
Loop Spaces ◽  
Infinite Loop Spaces ◽  
Infinite Loop ◽  
Plus Construction

Abstract We study quotients of mapping class groups ${\Gamma _{g,1}}$ of oriented surfaces with one boundary component by the subgroups ${{\cal I}_{g,1}}(k)$ in the Johnson filtrations, and we show that the stable classifying spaces ${\mathbb {Z}} \times B{({\Gamma _\infty }/{{\cal I}_\infty }(k))^ + }$ after plus-construction are infinite loop spaces, fitting into a tower of infinite loop space maps that interpolates between the infinite loop spaces ${\mathbb {Z}} \times B\Gamma _\infty ^ + $ and ${\mathbb {Z}} \times B{({\Gamma _\infty }/{{\cal I}_\infty }(1))^ + } \simeq {\mathbb {Z}} \times B{\rm{Sp}}{({\mathbb {Z}})^ + }$ . We also show that for each level k of the Johnson filtration, the homology of these quotients with suitable systems of twisted coefficients stabilises as the genus of the surface goes to infinity.

scholarly journals Spherical alterations of handles: embedding the manifold plus construction

2013 ◽  
Vol 13 (1) ◽  
pp. 35-60 ◽  
Author(s):  
Craig R Guilbault ◽  
Frederick C Tinsley
Keyword(s):  
Plus Construction
Sign in / Sign up

Export Citation Format

Share Document