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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.
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
We study configuration space integral formulas for Milnors homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. Our proof is essentially a combinatorial analysis of a certain space of
The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally compact topologi
We develop a spectral sequence for the homotopy groups of Loday constructions with respect to twisted products in the case where the group involved is a constant simplicial group. We show that for commutative Hopf algebra spectra Loday constructions
In this note we prove the analogue of the Atiyah-Segal completion theorem for equivariant twisted K-theory in the setting of an arbitrary compact Lie group G and an arbitrary twisting of the usually considered type. The theorem generalizes a result b