Some constructions, related to noncommutative tori; Fredholm modules and the Beilinson-Bloch regulator

Victor Kasatkin

Abstract: This PhD thesis covers the following 3 topics. (1) Explicit formulas for representatives of elements in a full set of generators for the odd K-theory of noncommutative 3-tori and 4-tori. (2) A variant of the graded-commutative framework of differential geometry for the polynomial subalgebra of the noncommutative torus algebra. (3) Closing a gap in the proof of a reconstruction of the Beilinson-Bloch regulator (for curves) via Fredholm modules given by Eugene Ha.