2004 Fiscal Year Final Research Report Summary
Homotopy equivalence and characterizations of subgroup complexes
| Project/Area Number |
13640021
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Woman's Christian University (2003-2004)
Osaka Kyoiku University (2001-2002) |
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Principal Investigator |
YOSHIARA Satoshi Tokyo Woman's Christian University, Department of Mathematics, Professor, 文理学部, 教授 (10230674)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Kazuaki Tokyo Woman's Christian University, Professor, 文理学部, 教授 (50031323)
OYAMA Nobuyuki Tokyo Woman's Christian University, Professor, 文理学部, 教授 (80223981)
YAMASHIMA Shigeho Tokyo Woman's Christian University, Associate Professor, 文理学部, 助教授 (80086347)
ISHIWATA Makiko Tokyo Woman's Christian University, Instructor, 文理学部, 助手 (80277095)
SUGIYAMA Masumi Tokyo Woman's Christian University, Instructor, 文理学部, 助手 (30086368)
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| Project Period (FY) |
2001 – 2004
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| Keywords | dimensional dual hyperoval / radical subgroup / generalized quadrangle / Monster / Fischer groups / homotopy equivalence / classifying space / subgroup complex |
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| Research Abstract |
I obtained the following results to projects (A)(1)-(3) and (B).
(A)Research of extended buildings and the related combinatorial structures.
(A-1)Characterization of extensions of buildings of spherical type, without assuming group actions : For the automorphism group of a generalized quadrangles acting regularly on its point set, its structure is severely restricted.
(A-2)Determination of the universal embeddings of related complexes : Many results on dimensional dual hyperovals-embeddings of dual circle geometries-are obtained, for example, the best upper bound for dimensions of their ambient spaces, fundamental properties and examples of those with metric, construction of sub dual hyperovals as substructures fixed by automorphisms, calculation of automorphism groups of known examples, and solutions for isomorphism problem between them.
(A-3)Research on the related functions on finite fields : Characteristic functions exploited in the construction of dual hyperovals by Buratti and Del Fra are classified.
(B)Construction of theory for homotopy equivalences of complexes of centric radical p-subgroups and its applications : (1)My project of determining radical subgroups for all sporadic simple groups is completed by determining those for the Monster and Baby Monster. (2)I made a contribution to the project by S.D.Smith and D.Benson for explicitly constructing classifying space for each sporadic simple group (for the Fischer groups). (3)The highest dimension of non-vanishing homology groups of p-subgroup complexes is determined for each prime p.
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