Description of the spectrum of fluctuations around a commutative vacuum solution, as well as around a solution with degenerate commutator in IIB matrix model is given in terms of supersymmetric Yang–Mills (YM) model. We construct explicitly the map and study the dependence of the spectrum and respective YM model on the symmetries of the solution. Introduction IKKT, or IIB matrix model [1], is a...

We continue the investigation of Hopf-Galois extensions with central invariants started in [30]. Our objective is not to imitate algebraic geometry using Hopf-Galois extension but to understand their geometric properties. Let H be a finite-dimensional Hopf algebra over a ground field k. Our main object of study is an H-Galois extension U ⊇ O such that O is a central subalgebra of U . Let us bri...

We give a general formula relating self cup products in cohomology to connecting maps in nonabelian cohomology, and apply it to obtain a formula for the self cup product associated to the Weil pairing.

The purpose of the following is to try to make sense of the stereographic projection in a non-commutative setup. To this end, we consider the open unit ball of a ternary ring of operators, which naturally comes equipped with a non-commutative version of a hyperbolic metric and ask for a manifold onto which the open unit ball can be mapped so that one might think of this situation as providing a...

Roughly speaking, $\mathbb{Z}_2^n$-manifolds are `manifolds' equipped with $\mathbb{Z}_2^n$-graded commutative coordinates the sign rule being determined by scalar product of their $\mathbb{Z}_2^n$-degrees. We examine notion a symplectic $\mathbb{Z}_2^n$-manifold, i.e., $\mathbb{Z}_2^n$-manifold two-form that may carry non-zero $\mathbb{Z}_2^n$-degree. show basic notions and results geometry ge...

We introduce a notion of crystalline cohomology for superschemes and show that it is isomorphic to the usual crystalline cohomology of the underlying commutative scheme if 2 is invertible on the base. Wess-Zumino terms play a crucial role in the matching of theoretical predictions in the framework of Quantum Chromodynamics of the decay of the neutral pion π into two photons π −→ γ + γ and the e...

We introduce a notion of crystalline cohomology for superschemes and show that it is isomorphic to the usual crystalline cohomology of the underlying commutative scheme if 2 is invertible on the base. Wess-Zumino terms play a crucial role in the matching of theoretical predictions in the framework of Quantum Chromodynamics of the decay of the neutral pion π into two photons π −→ γ + γ and the e...

We compare Mishchenko's definition of non-commutative signature for an oriented manifold with orientation preserving proper action a discrete, countable group $G$ the (more analytical) counterpart defined by Higson and Roe in series articles ``Mapping surgery to analysis''. A generalization bordism invariance coarse index is also addressed.

0. Introduction. Let M be a simply connected closed oriented n-dimensional manifold, and LM := Map C ∞ (S 1 , M) the associated free loop space. String topology of Chas and Sul-livan [CS] deals with an ample family of algebraic operations on the ordinary and equivariant homologies of LM , the most important being a graded commutative associative product,