Transchromatic extensions in motivic bordism Journal Article uri icon

Overview

abstract

  • We show a number of Toda brackets in the homotopy of the motivic bordism spectrum ; ; ; ; M; G; L; ; MGL; ; ; and of the Real bordism spectrum ; ; ; ; M; ; U; ; ; R; ; ; ; ; MU_{mathbb R}; ; ; . These brackets are ��red-shifting” in the sense that while the terms in the bracket will be of some chromatic height ; ; ; n; n; ; ; , the bracket itself will be of chromatic height ; ; ; ; (; n; +; 1; ); ; (n+1); ; ; . Using these, we deduce a family of exotic multiplications in the ; ; ; ; ; π; ; (; ; ,; ; ); ; ; M; G; L; ; pi _{(ast ,ast )}MGL; ; ; -module structure of the motivic Morava ; ; ; K; K; ; ; -theories, including non-trivial multiplications by ; ; ; 2; 2; ; ; . These in turn imply the analogous family of exotic multiplications in the ; ; ; ; ; π; ; ; ; ; M; ; U; ; R; ; ; ; pi _{star }MU_mathbb R; ; ; -module structure on the Real Morava ; ; ; K; K; ; ; -theories.

publication date

  • March 29, 2023

has restriction

  • gold

Date in CU Experts

  • October 17, 2023 7:01 AM

Full Author List

  • Beaudry A; Hill M; Shi XD; Zeng M

author count

  • 4

Other Profiles

Electronic International Standard Serial Number (EISSN)

  • 2330-1511

Additional Document Info

start page

  • 76

end page

  • 90

volume

  • 10

issue

  • 7