Related papers: The development of the princial genus theorem
This paper presents a commutative complex-oriented cohomology theory that realizes the Buchstaber formal group law localized away from 2. Also, the restriction of the classifying map of FB on special unitary cobordism ring localized away…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We generalize the Generic Model Theorem for equivariant presheaves of structures; extending the results of Macintyre and Caicedo. We also introduce a new class of generic cohomologies and show how, for some examples, they simplify to non…
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…
New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the…
Generalised characteristic classes are constructed for bordism cohomologies which allow a natural extension of classical genera to these bordism cohomology rings taking values in singular cohomology.
We propose a conceptually economical and computationally tractable completion of the foundations of gauge theory on quantum principal bundles \`{a} la Brzezi\'{n}ski--Majid to the case of general differential calculi and strong bimodule…
In this paper we introduce the notion of (pointed) prenormal category, modelled after regular categories, but with the key notions of coequaliser and kernel pair replaced by those of cokernel and kernel. This framework provides a natural…
Genus Theory is a classical feature of integral binary quadratic forms. Using the author's generalization of the well-known correspondence between quadratic form classes and ideal classes of quadratic algebras, we extend it to the case when…
We compute the genus of a rational quadratic form in terms of the K-theory of a C*-algebra attached to the adelic orthogonal group of the form. As a corollary, one gets a higher composition law for the rational quadratic forms. As an…
We construct a ring structure on complex cobordism tensored with the rationals, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-…
In this article, we prove a generalisation of the Mertens theorem for prime numbers to number fields and algebraic varieties over finite fields, paying attention to the genus of the field (or the Betti numbers of the variety), in order to…
We introduce the universal unitarily graded A-algebra for a commutative ring A and an arbitrary abelian extension U of the group of units of A, and use this concept to give simplified proofs of the main theorems of co-Galois theory in the…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, which in turn implies the existence of a ``universal generating…
In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds provides the conventional language of dynamic…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
Motivated by our attempt to understand characteristic classes of Lie groupoids and geometric structures, we are brought back to the fundamentals of the cohomology theories of Lie groupoids and algebroids. One element that was missing in the…
In the early 1970s, after a slow start, and lots of hurdles, Quantum Field Theory emerged as the superior doctrine for understanding the interactions between relativistic sub-atomic particles. After the conditions for a relativistic field…
In this paper we obtain the extended genus field of a global field. First we define the extended genus field of a global function field and we obtain, via class field theory, the description of the extended genus field of an arbitrary…