An interpolation between algebraic and special linear algebraic (co)bordism

Speaker: Ahina Nandy – Osnabrück University

Title: An interpolation between the algebraic (co)bordism spectrum $MGL$, and the special linear algebraic (co)bordism spectrum $MSL$

Abstract: Just like the universal complex oriented cohomology theory, complex cobordism ($MU$), we have a similar notion of universal oriented cohomology theory in the realm of stable $A^1$-homotopy theory. Algebraic cobordism ($MGL$) would be our analog of $MU$. Similar to $SU$-(co)bordism $MSU$, there is a notion of “universal” special linear oriented theory in motivic world. $MSL$ or special linear algebraic (co)bordism plays the role of $MSU$ here. I would like to talk a bit more about $MSL$. Conner-Floyd determined the torsions in $SU$-bordism already back in the late 60’s. The main ingredient of their work was an interpolation between $MSU$ and $MU$. It results into a filtration of $MU$ in terms of $MSU$ and facilitates further computation. I will talk about an exactly similar interpolation between $MSL$ and $MGL$ we have shown. Now, I am trying to use this filtration and the resulting spectral sequence to get some information about stable homotopy groups of $MSL$. I would also like to talk a bit about that.