The 2-Completion of L-Theory for C-Algebras

Explore advanced concepts in algebraic topology and K-theory through this in-depth lecture on the 2-completion of L-theory for C*-algebras. Delve into joint work with Thomas Nikolaus, examining the relationship between algebraic K-theory and L-theory spectra for rings with involution. Investigate the Tate construction of C2-actions on algebraic K-theory spectra and its connection to symmetric projective L-theory. Focus on the case of complex C*-algebras, analyzing the map between algebraic and topological K-theory spectra. Discover how the composite map from L-theory to the Tate construction of topological K-theory relates to 2-completion. Gain insights into the natural map between topological K-theory and L-theory spectra, including its effects on homotopy groups. Explore potential connections to real algebraic K-theory and Atiyah-Segal completion questions, time permitting. Enhance your understanding of advanced mathematical concepts in topology, K-theory, and C*-algebras through this comprehensive lecture from the Hausdorff Trimester Program on Topology.