We introduce a 2-cocycle for symplectic and skew-hermitian hyperbolic groups over arbitrary fields and skew fields, with values in the Witt group of hermitian forms. This cocycle has good functorial properties: it is natural under extension of scalars and stable, so it can be viewed as a universal 2-dimensional characteristic class for these groups. Over R and C, it coincides with the first Che...

We introduce a 2-cocycle for symplectic and skew-hermitian hyperbolic groups over arbitrary fields and skew fields, with values in the Witt group of hermitian forms. This cocycle has good functorial properties: it is natural under extension of scalars and stable, so it can be viewed as a universal 2-dimensional characteristic class for these groups. Over R and C, it coincides with the first Che...

The Bott–Thurston cocycle is a $$2$$ -cocycle on the group of orientation-preserving diffeomorphisms circle. We introduce and study formal analog cocycle. continuous $$A$$ -automorphisms algebra $$A((t))$$ Laurent series over commutative ring with values in $$A^*$$ invertible elements . prove that central extension given by equivalent to 12-fold Baer sum determinantal when $$\mathbb Q$$ -algebr...

We study a 1-cocycle on the fatgraph complex of punctured surface introduced by Penner. present an explicit cobounding cochain for this cocycle, whose formula involves summation over trivalent vertices spine. In similar fashion, we express symplectic form underlying given

We study cocycle properties of vertex operators and present an operator representation of cocycle operators, which are attached to vertex operators to ensure the duality of amplitudes. It is shown that this analysis makes it possible to obtain the general class of consistent string theories on orbifolds. ∗ To appear in the proceedings of YITP Workshop on “Recent Developments in String and Field...

We derive bivariate polynomial formulae for cocycles and coboundaries in Z(Zp , Zp ), and a basis for the (p − 1 − n)-dimensional GF (p)-space of coboundaries. When p = 2we determine a basis for the (2+ ( n 2 ) −1)-dimensional GF (2)-space of cocycles and show each cocycle has a unique decomposition as a direct sum of a coboundary and a multiplicative cocycle of restricted form.

We show that the spectral action, when perturbed by a gauge potential, can be written as series of Chern–Simons actions and Yang–Mills all orders. In odd orders, generalized forms are integrated against an $(b,B)$-cocycle, whereas, in even powers curvature $(b,B)$-cocycles Hochschild cocycles well. both cases, cochains derived from Taylor expansion action $\\operatorname{Tr}(f(D+V))$ $V=\\pi_D(...