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Abstract:

In 1969 R.H. Bing asked the following question: Is there a compact two-dimensional polyhedron with the fixed point property which has even Euler characteristic? In this paper we prove that there are no spaces with these properties and abelian fundamental group. We also show that the fundamental group of such a complex cannot have trivial Schur multiplier. © 2016 Elsevier Inc.

Registro:

Documento: Artículo
Título:On a question of R.H. Bing concerning the fixed point property for two-dimensional polyhedra
Autor:Barmak, J.A.; Sadofschi Costa, I.
Filiación:Departamento de Matematica, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Fixed point property; Homotopy classification; Nielsen fixed point theory; Two-dimensional complexes
Año:2017
Volumen:305
Página de inicio:339
Página de fin:350
DOI: http://dx.doi.org/10.1016/j.aim.2016.09.025
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_00018708_v305_n_p339_Barmak

Referencias:

  • Bing, R.H., The elusive fixed point property (1969) Amer. Math. Monthly, 76, pp. 119-132
  • Brown, R.F., The Lefschetz Fixed Point Theorem (1971), Scott, Foresman and Co. Glenview, Ill.–London vi+186 pp; Brown, K.S., Cohomology of Groups (1982) Graduate Texts in Mathematics, 87. , Springer-Verlag New York–Berlin x+306 pp
  • Dold, A., Lectures on Algebraic Topology (1980), second edition Springer-Verlag Berlin–New York xi+377 pp; Gorenstein, D., Lyons, R., Solomon, R., The classification of the finite simple groups. Number 3. Part I. Chapter A. Almost simple K-groups (1998) Mathematical Surveys and Monographs, vol. 40.3. , Amer. Math. Soc. Providence, RI xvi+419 pp
  • Gutierrez, M., Latiolais, M.P., Partial homotopy type of finite two-complexes (1991) Math. Z., 207, pp. 359-378
  • Hagopian, C.L., An update on the elusive fixed-point property (2007) Open Problems in Topology. II, pp. 263-277. , E. Pearl Elsevier B. V
  • Hambleton, I., Kreck, M., Cancellation of lattices and finite two-complexes (1993) J. Reine Angew. Math., 442, pp. 91-109
  • Hog-Angeloni, C., Metzler, W., Sieradski, A.J., (1993) Two Dimensional Homotopy and Combinatorial Group Theory, London Math. Soc. Lecture Note Series, 197. , Cambridge University Press Cambridge xii+412 pp
  • Jiang, B., On the least number of fixed points (1980) Amer. J. Math., 102, pp. 749-763
  • Jiang, B., Lectures on Nielsen Fixed Point Theory (1983) Contemp. Math., 14. , Amer. Math. Soc. Providence, RI vii+110 pp
  • Lopez, W., An example in the fixed point theory of polyhedra (1967) Bull. Amer. Math. Soc., 73, pp. 922-924
  • Spanier, E., Algebraic Topology (1966), McGraw-Hill Book Co. New York–Toronto, Ont.–London xiv+528 pp; Waggoner, R., A fixed point theorem for (n−2)-connected n-polyhedra (1972) Proc. Amer. Math. Soc., 33, pp. 143-145
  • Waggoner, R., A method of combining fixed points (1975) Proc. Amer. Math. Soc., 51, pp. 191-197
  • Weibel, C.A., An Introduction to Homological Algebra (1994) Cambridge Studies in Advanced Mathematics, 38. , Cambridge University Press Cambridge xiv+450 pp

Citas:

---------- APA ----------
Barmak, J.A. & Sadofschi Costa, I. (2017) . On a question of R.H. Bing concerning the fixed point property for two-dimensional polyhedra. Advances in Mathematics, 305, 339-350.
http://dx.doi.org/10.1016/j.aim.2016.09.025
---------- CHICAGO ----------
Barmak, J.A., Sadofschi Costa, I. "On a question of R.H. Bing concerning the fixed point property for two-dimensional polyhedra" . Advances in Mathematics 305 (2017) : 339-350.
http://dx.doi.org/10.1016/j.aim.2016.09.025
---------- MLA ----------
Barmak, J.A., Sadofschi Costa, I. "On a question of R.H. Bing concerning the fixed point property for two-dimensional polyhedra" . Advances in Mathematics, vol. 305, 2017, pp. 339-350.
http://dx.doi.org/10.1016/j.aim.2016.09.025
---------- VANCOUVER ----------
Barmak, J.A., Sadofschi Costa, I. On a question of R.H. Bing concerning the fixed point property for two-dimensional polyhedra. Adv. Math. 2017;305:339-350.
http://dx.doi.org/10.1016/j.aim.2016.09.025