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Abstract:

We investigate a stronger formulation of Webb's conjecture on the contractibility of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more recently, by Bux, Libman and Linckelmann, can be restated in terms of the topology of certain finite spaces. We propose a stronger conjecture, and prove various particular cases by combining fusion theory of finite groups and homotopy theory of finite spaces. © 2019 Elsevier Inc.

Registro:

Documento: Artículo
Título:A stronger reformulation of Webb's conjecture in terms of finite topological spaces
Autor:Piterman, K.I.
Filiación:Departamento de Matemática, IMAS-CONICET, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Finite topological spaces; Fusion; Orbit spaces; p-Subgroups; Posets
Año:2019
Volumen:527
Página de inicio:280
Página de fin:305
DOI: http://dx.doi.org/10.1016/j.jalgebra.2019.02.037
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v527_n_p280_Piterman

Referencias:

  • Aschbacher, M., Kessar, R., Oliver, B., Fusion Systems in Algebra and Topology (2011) London Mathematical Society Lecture Notes, 391. , Cambridge University Press Cambridge vi+320 pp
  • Aschbacher, M., Kleidman, P.B., On a conjecture of Quillen and a lemma of Robinson (1990) Arch. Math. (Basel), 55 (3), pp. 209-217
  • Aschbacher, M., Smith, S.D., On Quillen's conjecture for the p-groups complex (1993) Ann. of Math. (2), 137 (3), pp. 473-529
  • Aschbacher, M., Simple connectivity of p-group complexes (1993) Israel J. Math., 82 (1-3), pp. 1-43
  • Barmak, J., Algebraic Topology of Finite Topological Spaces and Applications (2011) Lecture Notes in Math., 2032. , Springer xviii+170
  • Barmak, J., Minian, E.G., Strong homotopy types, nerves, and collapses (2012) Discrete Comput. Geom., 47 (2), pp. 301-328
  • Bouc, S., Homologie de certains ensembles ordonnés (1984) C. R. Acad. Sci. Paris Sér. I Math., 299 (2), pp. 49-52
  • Bredon, G.E., Introduction to Compact Transformation Groups (1972) Pure Appl. Math., 46. , Academic Press San Diego xiii+459
  • Brown, K., Euler characteristics of groups: the p-fractional part (1975) Invent. Math., 29 (1), pp. 1-5
  • Bux, K.-U., Orbit Spaces of Subgroup Complexes, Morse Theory, and a New Proof of a Conjecture of Webb (1999) Topology Proceedings, 24, pp. 39-51
  • Craven, D.A., The Theory Of Fusion Systems: an Algebraic Approach (2011) Cambridge Studies in Advanced Mathematics, 131. , Cambridge University Press Cambridge xii+371 pp
  • (2016), A. Díaz Ramos, On Quillen's conjecture for p-solvable groups, preprint; GAP – Groups, Algorithms, and Programming (2014), http://www.gap-system.org, Version 4.7.6; Hawkes, T., Isaacs, I.M., On the poset of p-subgroups of a p-solvable group (1988) J. Lond. Math. Soc. (2), 38 (1), pp. 77-86
  • Ksontini, R., Simple connectivity of the Quillen complex of the symmetric group (2003) J. Combin. Theory Ser. A, 103, pp. 257-279
  • Ksontini, R., The fundamental group of the Quillen complex of the symmetric group (2004) J. Algebra, 282 (1), pp. 33-57
  • Libman, A., Webb's conjecture for fusion systems (2008) Israel J. Math., 167, pp. 141-154
  • Linckelmann, M., The orbit space of a fusion system is contractible (2009) Proc. Lond. Math. Soc. (3), 98, pp. 191-216
  • McCord, M.C., Singular homology groups and homotopy groups of finite topological spaces (1966) Duke Math. J., 33, pp. 465-474
  • Minian, E.G., Piterman, K.I., The homotopy types of the posets of p-subgroups of a finite group (2018) Adv. Math., 328, pp. 1217-1233
  • Quillen, D., Homotopy properties of the poset of nontrivial p-subgroups of a group (1978) Adv. Math., 28, pp. 101-128
  • SageMath, the Sage Mathematics Software System (2016), http://www.sagemath.org, Version 7.6, the Sage Developers; Smith, S.D., Subgroup Complexes (2011) Mathematical Surveys and Monographs, 179. , Amer. Math. Soc. Providence, RI xii+364
  • Stong, R.E., Finite topological spaces (1966) Trans. Amer. Math. Soc., 123, pp. 325-340
  • Stong, R.E., Group actions on finite spaces (1984) Discrete Math., 49, pp. 95-100
  • Symonds, P., The orbit space of the p-subgroup complex is contractible (1998) Comment. Math. Helv., 73 (3), pp. 400-405
  • Thévenaz, J., Webb, P.J., Homotopy equivalence of posets with a group action (1991) J. Combin. Theory Ser. A, 56 (2), pp. 173-181
  • Webb, P.J., Subgroup complexes (1987) The Arcata Conference on Representations of Finite Groups, Arcata, Calif., 1986, Proc. Sympos. Pure Math., 47, pp. 349-365. , Amer. Math. Soc. Providence, RI

Citas:

---------- APA ----------
(2019) . A stronger reformulation of Webb's conjecture in terms of finite topological spaces. Journal of Algebra, 527, 280-305.
http://dx.doi.org/10.1016/j.jalgebra.2019.02.037
---------- CHICAGO ----------
Piterman, K.I. "A stronger reformulation of Webb's conjecture in terms of finite topological spaces" . Journal of Algebra 527 (2019) : 280-305.
http://dx.doi.org/10.1016/j.jalgebra.2019.02.037
---------- MLA ----------
Piterman, K.I. "A stronger reformulation of Webb's conjecture in terms of finite topological spaces" . Journal of Algebra, vol. 527, 2019, pp. 280-305.
http://dx.doi.org/10.1016/j.jalgebra.2019.02.037
---------- VANCOUVER ----------
Piterman, K.I. A stronger reformulation of Webb's conjecture in terms of finite topological spaces. J. Algebra. 2019;527:280-305.
http://dx.doi.org/10.1016/j.jalgebra.2019.02.037