Abstract. We define an “S -Euler characteristic”, χ̃S1 (X) , of a circle action on a compact manifold or finite complex X . It lies in the first Hochschild homology group HH1(ZG) where G is the fundamental group of X . This χ̃S1 (X) is analogous in many ways to the ordinary Euler characteristic. One application is an intuitively satisfying formula for the Euler class (integer coefficients) of the...

Using the lattice-theoretic version of the Euler characteristic introduced by V. Klee and G.-C. Rota in the Sixties, we define the Euler characteristic of a formula in Gödel logic (over finitely or infinitely many truth-values). We then prove that the information encoded by the Euler characteristic is classical, i.e. coincides with the analogous notion defined over Boolean logic. Building on th...

For a black hole’s spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the...

In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between the Euler numbers and the second kind stirling numbers. §

We prove a surgery formula for renormalized Euler characteristic of Ozsváth and Szabó. Equality χ̂ = −SW between this Euler cahracteristic and the Seiberg-Witten invariant follows for rational homology three-spheres. AMS Classification 57R58; 57Q10, 57R57, 53D40

In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the Euler characteristic of complete intersections in reductive groups. In the case where the complete intersection is a curve, this formula gives an explicit answer for the Euler characteristi...

We prove a surgery formula for renormalized Euler characteristic of Ozsváth and Szabó. The equality χ̂ = SW between this Euler cahracteristic and the Seiberg-Witten invariant follows for rational homology three-spheres.