Motivic Analogues of MO and MSO

Motivic homotopy theory;G-equivariant homotopy theory;Stable homotopy theory;Cobordism theories;homotopy type;Mathematics;Science;Mathematics

Ellis Jr, DondiSmith, Karen E ;

University of Michigan

关键词: Motivic homotopy theory;    G-equivariant homotopy theory;    Stable homotopy theory;    Cobordism theories;    homotopy type;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/137115/dondi_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis makes progress in computing the coefficients of Algebraic Hermitian Cobordism (MGLR), a motivic Z/2-equivariant spectrum constructed by P. Hu, I. Kriz, and K. Ormsby. In the process of my research, I realized it would be possible to construct motivic analogues of unoriented and oriented cobordism, which I refer to as MGLO and MSLO respectively. In chapters 2-3 of my thesis, I construct MGLO and MLSO and give a concrete description of the homotopy groups of each of them.In particular, my work on MGLO gives an answer to a question of Jack Morava. Using the tools of Tate cohomology and my computation of the coefficients of MGLO, the thesis ends with a computation of a localization of the homotopy groups of MGLR.