Equivariant cohomology and analytic descriptions of ring isomorphisms

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a $G$-manifold in terms of algebra, so that we can obtain analytic descriptions of ring isomorphisms among equivariant cohomology rings of such $G$-manifolds, and a necessary and sufficient condition that the equivariant cohomology rings of such two $G$-manifolds are isomorphic. This also leads us to analyze how many there are equivariant cohomology rings up to isomorphism for such $G$-manifolds in 2- and 3-dimensional cases.Comment: 20 pages, updated version with two references adde

Orbit spaces of free involutions on the product of two projective spaces

Let $X$ be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on $X$ and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray spectral sequence associated to the Borel fibration $X \hookrightarrow X_{\mathbb{Z}_2} \longrightarrow B_{\mathbb{Z}_2}$. We also give an application of our result to show that if $X$ has the mod 2 cohomology algebra of the product of two real projective spaces (respectively complex projective spaces), then there does not exist any $\mathbb{Z}_2$-equivariant map from $\mathbb{S}^k \to X$ for $k \geq 2$ (respectively $k \geq 3$), where $\mathbb{S}^k$ is equipped with the antipodal involution.Comment: 14 pages, to appear in Results in Mathematic

Transverse momentum spectra of charged particles in proton-proton collisions at s=900\sqrt{s} = 900 GeV with ALICE at the LHC

The inclusive charged particle transverse momentum distribution is measured in proton-proton collisions at $\sqrt{s} = 900$ GeV at the LHC using the ALICE detector. The measurement is performed in the central pseudorapidity region $(|\eta|<0.8)$ over the transverse momentum range $0.15<p_{\rm T}<10$ GeV/$c$. The correlation between transverse momentum and particle multiplicity is also studied. Results are presented for inelastic (INEL) and non-single-diffractive (NSD) events. The average transverse momentum for $|\eta|<0.8$ is $\left<p_{\rm T}\right>_{\rm INEL}=0.483\pm0.001$ (stat.) $\pm0.007$ (syst.) GeV/$c$ and \left_{\rm NSD}=0.489\pm0.001 (stat.) $\pm0.007$ (syst.) GeV/$c$, respectively. The data exhibit a slightly larger $\left<p_{\rm T}\right>$ than measurements in wider pseudorapidity intervals. The results are compared to simulations with the Monte Carlo event generators PYTHIA and PHOJET.Comment: 20 pages, 8 figures, 2 tables, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/390