On the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of classifying spaces of spinor groups

We compute the cotorsion product of the mod 2 cohomology of spinor group spin(n), which is the E_2-term of the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of the classifying space of the spinor group spin(n). As a consequence of this computation, we show the non-collapsing of the Rothenberg-Steenrod spectral sequence for n > 16.Comment: This is the version published by Geometry & Topology Monographs on 25 February 200

On the Rothenberg-Steenrod spectral sequence for the mod 3 cohomology of the classifying space of the exceptional Lie group E_8

We show that the Rothenberg--Steenrod spectral sequence converging to the mod 3 cohomology of the classifying space of the exceptional Lie group E_8 does not collapse at the E_2-level.Comment: This is the version published by Geometry & Topology Monographs on 29 January 200

On the cellular decomposition and the Lusternik-Schnirelmann category of Spin(7)Spin(7)

We give a cellular decomposition of the compact connected Lie group $Spin(7)$. We also determine the L-S categories of $Spin(7)$ and $Spin(8)$.Comment: 14 page

Lusternik-Schnirelmann categories of non-simply connected compact simple Lie groups

Let $F \hookrightarrow X \to B$ be a fibre bundle with structure group $G$, where $B$ is $(d{-}1)$-connected and of finite dimension, $d \geq 1$. We prove that the strong L-S category of $X$ is less than or equal to $m + \frac{\dim B}{d}$, if $F$ has a cone decomposition of length $m$ under a compatibility condition with the action of $G$ on $F$. This gives a consistent prospect to determine the L-S category of non-simply connected Lie groups. For example, we obtain \cat{PU(n)} \leq 3(n{-}1) for all $n \geq 1$, which might be best possible, since we have \cat{\mathrm{PU}(p^r)}=3(p^r{-}1) for any prime $p$ and $r \geq 1$. Similarly, we obtain the L-S category of $\mathrm{SO}(n)$ for $n \leq 9$ and $\mathrm{PO}(8)$. We remark that all the above Lie groups satisfy the Ganea conjecture on L-S category.Comment: 13 page

Integral cohomology and chern classes of the special linear group over the ring of integers

This paper is devoted to the complete calculation of the additive structure of the 2-torsion of the integral cohomology of the innite special linear group SL(Z) over the ring of integers Z. This enables us to determine the best upper bound for the order of the Chern classes of all integral and rational representations of discrete groups.</p

On the Lusternik-Schnirelmann category of symmetric spaces of classical type

We determine the Lusternik-Schnirelmann category of the irreducible, symmetric Riemann spaces SU(n)/SO(n) and SU(2n)/Sp(n) of type AI and AII respectively.Comment: This is the version published by Geometry & Topology Monographs on 25 February 200

On the Stiefel-Whitney classes of the representations associated with Spin(15)

We determine the Stiefel-Whitney classes of the second exterior representation and the spin representation of Spin(15), which are useful to calculate the mod 2 cohomology of the classifying space of the exceptional Lie group E_8.Comment: This is the version published by Geometry & Topology Monographs on 14 November 200

Geotechnical approaches for preservation of openly exhibited Geo-relics damaged by rainfall infiltration

Excavated geo-relics are vulnerable to damage by natural processes. The aim of this study is to contribute to the establishment of a technical framework for the preservation of openly exhibited geo-relics. This study also examines the preservation of an openly exhibited geo-relic in Japan, which has experienced surface deformation in the soft soil layer due to water infiltration. The surface deformation is numerically investigated by performing seepage-deformation analyses based on unsaturated soil mechanics in order to understand its mechanism and to obtain effective countermeasures. The results show that deformation develops in the surface layer of the slope as the bonding between soil particles, represented by skeleton stress, and decreases when water infiltrates the slope. Although the calculation considers the influence of groundwater, as well as precipitation, the results show that the deformation of the slope is primarily controlled by precipitation, not by groundwater. Furthermore, the elevation of the groundwater does not contribute to the development of surface deformation. Based on the mechanism of the surface deformation, replacing the surface layer with a well-compacted, highly permeable soil is proposed to improve slope stability. It is predicted that this proposed method will be effective because the replaced zone retains sufficient strength and stiffness when it is wet, despite a decrease in the skeleton stress due to rainfall infiltration. This countermeasure has been adopted for the actual restoration of a damaged slope