• Title, Summary, Keyword: classifying spaces

Search Result 36, Processing Time 0.03 seconds

COFINITE PROPER CLASSIFYING SPACES FOR LATTICES IN SEMISIMPLE LIE GROUPS OF ℝ-RANK 1

  • Kang, Hyosang
    • Communications of the Korean Mathematical Society
    • /
    • v.32 no.3
    • /
    • pp.745-763
    • /
    • 2017
  • The Borel-Serre partial compactification gives cofinite models for the proper classifying space for arithmetic lattices. Non-arithmetic lattices arise only in semisimple Lie groups of ${\mathbb{R}}$-rank one. The author generalizes the Borel-Serre partial compactification to construct cofinite models for the proper classifying space for lattices in semisimple Lie groups of ${\mathbb{R}}$-rank one by using the reduction theory of Garland and Raghunathan.

Margolis homology and morava K-theory of classifying spaces for finite group

  • Cha, Jun-Sim
    • Journal of the Korean Mathematical Society
    • /
    • v.32 no.3
    • /
    • pp.563-571
    • /
    • 1995
  • The recent work of Hopkins, Kuhn and Ravenel [H-K-R] indicates the Morava K-theory, $K(n)^*(-)$, occupy an important and fundamental place in homology theory. In particular $K(n)^*(BG)$ for classifying spaces of finite groups are studied by many authors [H-K-R], [R], [T-Y 1, 2] and [Hu].

  • PDF

SPLITTINGS FOR THE BRAID-PERMUTATION GROUP

  • Jeong, Chan-Seok;Song, Yong-Jin
    • Journal of the Korean Mathematical Society
    • /
    • v.40 no.2
    • /
    • pp.179-193
    • /
    • 2003
  • The braid-permutation group is a group of welded braids which is the extension of Artin's braid groups by the symmetric groups. It is also described as a subgroup of the automorphism group of a free group. We also show that the plus-construction of the classifying space of the infinite braid-permutation group has the following two types of splittings BBP(equation omitted) B∑(equation omitted) $\times$ X, BBP(equation omitted) B $^{+}$$\times$ Y=S$^1$$\times$Y, where X, Y are some spaces.

The Evaluation and the Classification of Zones for Setting Additional Green Spaces (녹지 잠재 영향권역 설정을 통한 녹지단절구역 분류 및 우선순위 선정)

  • Sagong Jung-Hee;Ra Jung-Hwa
    • Journal of the Korean Institute of Landscape Architecture
    • /
    • v.33 no.2
    • /
    • pp.1-15
    • /
    • 2005
  • The purpose of this paper is to classify zones disrupting green spaces in city and to evaluate of their grades. The results are as follows; L There were 158 green spaces in Dalsu-gu. The 158 green spaces were classified 4 patterns and minutely classified into 9 types. The area of the 'nature park' type was turned out to be $70.1\%$ of the total area of green spaces in Dalsu-gu, then the type was considered as a important part of the green-network in Dalsu-gu. The 9 types such as 'nature park', 'river', 'neighborhood park' and so on were analysed with ecological indexes. 2. Based on the ecological indexes of 'ratio of the green space', 'features of the surrounding matrix' and 'travel distance of the wildlives' , zones disrupting green spaces were ranging widely and re-divided to 236 sectors. 3. The analysis results for classifying the grades were that grade I appeared over industrial complex and housing complex widely. On the other side, grade II and III appeared around or between nature park and neighboring park Consequently, it was necessary to consider the grade and make zones disrupting green spaces into green space for improving green network.

A Survey on the Spaces in Police Substation for Improving Area Standards (지역경찰관서 면적기준 개선을 위한 실태조사)

  • Kang, Kyung-Yeon;Han, Gi-Sung;Lee, Kyung-Hoon
    • Journal of the Architectural Institute of Korea Planning & Design
    • /
    • v.36 no.2
    • /
    • pp.3-11
    • /
    • 2020
  • The police substation includes work spaces for civil services, interviews, and meetings, etc, and private spaces for rest, showers and cafeterias and so on. Since a large number of rooms for each function should be installed in a relatively small building, it is important to develop an area standard for efficient space organization in consideration of the functional characteristics and usage patterns of each space. The purpose of this study is to suggest the way for improving the area standards for spaces in police substation based on the results of existing standards analysis and case study. For this objective, architectural documents of 161 police substations built after 2013 in Korea were comparatively analyzed. Sixteen of these facilities were selected for field survey and investigated how the workspace and private area were organized and used. The results of investigation showed that there were a number of problematic cases, such as spaces not installed or insufficient, spaces used for two or more functions, spaces installed even though they are not included in the standards. It was mainly due to the fact that several important spaces which had been installed in most police substations were not included in the existing standards. The ways for improvement were suggested like following four points: (1) Modifying the criteria for classifying facility size, (2) Modifying the lists of the required spaces, (3) Specifying the basis of calculation for each space in detail, and (4) Differentiating the way to organize spaces according to the facility size.

STABLE SPLITTINGS OF BG FOR GROUPS WITH PERIODIC COHOMOLOGY AND UNIVERSAL STABLE ELEMENTS

  • Lim, Pyung-Ki
    • Bulletin of the Korean Mathematical Society
    • /
    • v.26 no.2
    • /
    • pp.109-114
    • /
    • 1989
  • This paper deals with the classifying spaces of finite groups. To any finite group G we associate a space BG with the property that .pi.$_{1}$(BG)=G, .pi.$_{i}$ (BG)=0 for i>1. BG is called the classifying space of G. Consider the problem of finding a stable splitting BG= $X_{1}$$^{V}$ $X_{1}$$^{V}$..$^{V}$ $X_{n}$ localized at pp. Ideally the $X_{i}$ 's are indecomposable, thus displaying the homotopy type of BG in the simplest terms. Such a decomposition naturally splits $H^{*}$(BG). The main purpose of this paper is to give the classification theorem in stable homotopy theory for groups with periodic cohomology i.e. cyclic Sylow p-subgroups for p an odd prime and to calculate some universal stable element. In this paper, all cohomology groups are with Z/p-coefficients and p is an odd prime.prime.

  • PDF

HOMOTOPY TYPE OF A 2-CATEGORY

  • Song, Yongjin
    • Korean Journal of Mathematics
    • /
    • v.18 no.2
    • /
    • pp.175-183
    • /
    • 2010
  • The classical group completion theorem states that under a certain condition the homology of ${\Omega}BM$ is computed by inverting ${\pi}_0M$ in the homology of M. McDuff and Segal extended this theorem in terms of homology fibration. Recently, more general group completion theorem for simplicial spaces was developed. In this paper, we construct a symmetric monoidal 2-category ${\mathcal{A}}$. The 1-morphisms of ${\mathcal{A}}$ are generated by three atomic 2-dimensional CW-complexes and the set of 2-morphisms is given by the group of path components of the space of homotopy equivalences of 1-morphisms. The main part of the paper is to compute the homotopy type of the group completion of the classifying space of ${\mathcal{A}}$, which is shown to be homotopy equivalent to ${\mathbb{Z}}{\times}BAut^+_{\infty}$.

A PROSET STRUCTURE INDUCED FROM HOMOTOPY CLASSES OF MAPS AND A CLASSIFICATION OF FIBRATIONS

  • Yamaguchi, Toshihiro;Yokura, Shoji
    • Communications of the Korean Mathematical Society
    • /
    • v.34 no.3
    • /
    • pp.991-1004
    • /
    • 2019
  • Firstly we consider preorders (not necessarily partial orders) on a canonical quotient of the set of the homotopy classes of continuous maps between two spaces induced by a certain equivalence relation ${\sim}_{{\varepsilon}R}$. Secondly we apply it to a classification of orientable fibrations over Y with fibre X. In the classification theorem of J. Stasheff [22] and G. Allaud [3], they use the set $[Y,\;Baut_1X]$ of homotopy classes of continuous maps from Y to $Baut_1X$, which is the classifying space for fibrations with fibre X due to A. Dold and R. Lashof [11]. In this paper we give a classification of fibrations using a preordered set (abbr., proset) structure induced by $[Y,\;Baut_1X]_{{\varepsilon}R}:=[Y,\;Baut_1X]/{\sim}_{{\varepsilon}R}$.

Existence of subpolynomial algebras in $H^*(BG,Z/p)$

  • Lee, Hyang-Sook;Shin, Dong-Sun
    • Bulletin of the Korean Mathematical Society
    • /
    • v.34 no.1
    • /
    • pp.1-8
    • /
    • 1997
  • Let G be a finiteg oroup. We denote BG a classifying space of G, which a contractible universal principal G bundle EG. The stable type of BG does not determine G up to isomorphism. A simple example [due to N. Minami]is given by $Q_{4p} \times Z/2$ and $D_{2p} \times Z/4$ where ps is an odd prime, $Q_{4p} is the generalized quarternion group of order 4p and $D_{2p}$ is the dihedral group of order 2p. However the paper [6] gives us a necessary and sufficient condition for $BG_1$ and $BG_2$ to be stably equivalent localized et pp. The local stable type of BG depends on the conjegacy classes of homomorphisms from the p-groups Q into G. This classification theorem simplifies if G has a normal sylow p-subgroup. Then the stable homotopy type depends on the Weyl group of the sylow p-subgroup.

  • PDF

A Preliminary Study on the Characteristics and Criteria of New Material for the Possibility of Application in Housing Space (주거공간에 적용 가능한 신소재 특성 및 기준에 관한 기초 연구)

  • Jung, Sun-Hee;Seo, Ji-Eun
    • Journal of the Korean housing association
    • /
    • v.21 no.4
    • /
    • pp.71-79
    • /
    • 2010
  • This study is a fundamental research which suggests some standards that can be used in selecting some advanced materials to be applied in housing space designs. The following conclusions have been drawn from the study. First, it has been discovered that as the residents' quality of life improved, the finishing materials emerged as an important element of housing spaces. It could also be seen that among the finishing materials used in housing spaces, there is recently a growing trend towards various environmentally-friendly advanced materials under the theme of 'the nature' and 'health'. As a result, the need to investigate the standards of discriminatory and efficient housing space designs using advanced materials is on the increase. Second, through the literature and precedent studies, the physical criteria of advanced materials have been classified into five categories: new technology, new manufacturing methods, new materials, complementation and applicability. The main criteria of advanced finishing materials for housing spaces have been classified into four main categories: durability, functionality, economical efficiency and sensibility. By collecting and classifying some key words according to each of these four categories, the representative or combinable features have been extracted. By organizing the advanced materials' physical criteria and their details, some standards based on the physical aspects have been suggested. The features of the finishing materials in consideration of advanced materials have been reclassified into the user-based criteria, environmental criteria and spatial criteria. Through this method, the criteria have been brought up from a new viewpoint, establishing the standards for the advanced materials applicable to housing spaces. Finally, after assessing the criteria by analyzing the advanced materials currently known to be applicable in housing spaces, it has been concluded that the criteria can be used as the fundamental standards. As this study is based on investigating the literature and data, it may be less than reasonable to generalize from the limited number of examples. Hence, it shall be important to make a profound study of some detailed criteria by suggesting more objective standards and analyzing a greater variety of advanced materials.