Spin^c Analysis for Group C^*-bundles on Manifolds and Study of Yamabe Invariants

点击翻译按钮获取中文摘要

We studied on Spin^c Analysis for Group C^*-bundles on Manifolds and Yamabe Invariants.More precisely, we studied on the fundamentals of C^*-algebras and their K-theory. We also studied on the synthetic research of Yamabe invariants and Bordism theory with supergroups (i.e., supergroups, supergroup-structures on manifolds, supergroup C^*-bunbles and others). In particular, by using this bordism theory with supergroups, we obtained an obstruction to the positivity of relative Yamabe invariants. This result is written in the following paper :Kazuo Akutagawa, An obstruction to the positivity of relative Yamabe invariants.The head investigator, Kazuo Akutagawa also studied with professor Boris Botvinnik (University of Oregon) on Yamabe invariants from the algebraic topological viewpoint. Similar to the Homology theory, we defined a natural relative version of the Yamabe invariant, that is, the "relative Yamabe invariant", and we studied on it and the relation of the Yamabe invariant of a double manifold. This result is also written in the following papers :Kazuo Akutagawa and Boris Botvinnik, Relative Yamabe invariant.Kazuo Akutagawa and Boris Botvinnik, Manifolds of positive scalar curvature and conformal cobordism theory.