Graduate School of
Science and Engineering

Homologically the same boundary groups configured with whole three-dimensional homological spheres are an important subject of research related to the unsolved expectation of triangles being divisible by high-dimensional manifolds, however, very little is known about the structure except the fact that it is a finitely generated Abelian group. My research involves homologically the same boundary invariants in seeking structures that particularly include the integer lifting of classic Rochlin invariants by applying gauge theory to V-manifolds. Gauge theory can be used to extract topology information from nonlinear partial differential equations describing the field (particle) on the manifold. I focus on the contribution made by the singular point of a Vmanifold and configure the integer lift of an Ochanine invariant based on elliptic genus and unbound algebra related to the same boundary of the three-dimensional manifold and the functor in a certain type of zone with a commutative ring in order to consider the relationship between basic group, homological algebra and gauge theory more.