Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLow dimensional Milnor-Witt stems over R
475
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This article computes some motivic stable homotopy groups over R. For 0 <= p - q <= 3, we describe the motivic stable homotopy groups of a completion of the motivic sphere spectrum. These are the first four Milnor-Witt stems. We start with the known Ext groups over C and apply the rho-Bockstein spectral sequence to obtain Ext groups over R. This is the input to an Adams spectral sequence, which collapses in our low dimensional range.
rate research
Read More
We compute some R-motivic stable homotopy groups. For $s - w leq 11$, we describe the motivic stable homotopy groups $pi_{s,w}$ of a completion of the R-motivic sphere spectrum. We apply the $rho$-Bockstein spectral sequence to obtain R-motivic Ext groups from the C-motivic Ext groups, which are well-understood in a large range. These Ext groups are the input to the R-motivic Adams spectral sequence. We fully analyze the Adams differentials in a range, and we also analyze hidden extensions by $rho$, 2, and $eta$. As a consequence of our computations, we recover Mahowald invariants of many low-dimensional classical stable homotopy elements.
We show that the $C_2$-equivariant and $mathbb{R}$-motivic stable homotopy groups are isomorphic in a range. This result supersedes previous work of Dugger and the third author.
We compute the stable homotopy groups up to dimension 90, except for some carefully enumerated uncertainties.
In this paper, we study {bf twisted Milnor hypersurfaces} and compute their $hat A$-genus and Atiyah-Singer-Milnor $alpha$-invariant. Our tool to compute the $alpha$-invariant is Zhangs analytic Rokhlin congruence formula. We also give some applications about group actions and metrics of positive scalar curvature on twisted Milnor hypersurfaces.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
