Relative Khovanov–Jacobsson classes

Relative natural classes and relative injectivity

Let τ be a hereditary torsion theory on the category R-Mod of left R-modules over an associative unitary ring R. We introduce the notion of τ-natural class as a class of modules closed under τ-dense submodules, direct sums, and τ-injective hulls. We study connections between certain conditions involving τ-(quasi-)injectivity in the context of τnatural classes, generalizing results established b...

Relative semicharacteristic classes

§0. Introduction In 1973 Ronnie Lee introduced the notion of semicharacteristic classes, which are invariants of the bordism group yi^(Bn) of closed manifolds equipped with a free action of a finite group n. In this paper we relativize his theory. Associated to a homomorphism G->n of finite groups, there is the relative bordism group yim(BG-> Bn), which is the bordism group of compact manifolds...

On the Relative Complexity of Post's Classes

Comparing complexity classes relative to physical oracles

We develop the idea of using a physical experiment as an oracle to an algorithm. As a case study, we compare the computational power of deterministic and non-deterministic Turing machines connected to a simple physical oracle, namely, the scatter machine experiment. We prove relativisation theorems for the conjectures concerning P , NP , PSPACE relative to this physical oracle. Finally, we refl...

Relative Bott-Chern Secondary Characteristic Classes

In this paper, we introduce six axioms for relative Bott-Chern secondary characteristic classes and prove the uniqueness and existence theorem for them. Such a work provides us a natural way to understand and hence to prove the arithmetic Grothendieck-Riemann-Roch theorem.