Abstract

We construct algebraic unoriented and oriented cobordism, named $\mathsf{MGLO}$ and $\mathsf{MSLO}$, respectively. $\mathsf{MGLO}$ is defined and its homotopy groups are explicitly computed, giving an answer to a question of Jack Morava. $\mathsf{MSLO}$ is also defined and its coefficients are explicitly computed after completing at a prime $p$. Similarly to $\mathsf{MSO}$, the homotopy type of $\mathsf{MSLO}$ depends on whether the prime $p$ is even or odd. Finally, a computation of a localization of the homotopy groups of $\mathsf{MGLR}$ is given.

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Mathematical Subject Classification 2010

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