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Abstract:

We investigate Whitehead’s asphericity question from a new perspective, using results and techniques of the homotopy theory of finite topological spaces. We also introduce a method of reduction to investigate asphericity based on the interaction between the combinatorics and the topology of finite spaces. © 2013, Tbilisi Centre for Mathematical Sciences.

Registro:

Documento: Artículo
Título:A new approach to Whitehead’s asphericity question
Autor:Cerdeiro, M.A.; Minian, E.G.
Filiación:Departamento de Matemática, IMAS, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:CW-complexes; Finite topological spaces; Posets; Simplicial complexes; Whitehead’s asphericity question
Año:2014
Volumen:9
Número:2
Página de inicio:339
Página de fin:348
DOI: http://dx.doi.org/10.1007/s40062-013-0031-x
Título revista:Journal of Homotopy and Related Structures
Título revista abreviado:J. Homotopy Related Struct.
ISSN:15122891
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15122891_v9_n2_p339_Cerdeiro

Referencias:

  • Barmak, J.A., Algebraic topology of finite topological spaces and applications (2011) Lecture Notes in Mathematics, 2032. , Springer, Berlin
  • Barmak, J.A., Minian, E.G., Simple homotopy types and finite spaces (2008) Adv. Math, 218 (1), pp. 87-104
  • Björner, A., Topological methods (1995) Handbook of Combinatorics, 2, pp. 1819-1872
  • Bogley, W., J.H.C. Whitehead’s asphericity question, in Two-dimensional homotopy and combinatorial group theory (1993) London Mathematical Society Lecture Note Series, 197. , Cambridge University Press, Cambridge
  • Cockcroft, W.H., On two dimensional aspherical complexes (1954) Proc. Lond. Math. Soc, 4 (3), pp. 375-384
  • Cohen, M.M., A course in simple homotopy theory (1973) Graduate Texts in Mathematics, 10. , Springer, New York, Berlin
  • Howie, J., Some remarks on a problem of J. H. C. Whitehead (1983) Topology, 22, pp. 475-485
  • Kozlov, D., Combinatorial Algebraic Topology (2008) Algorithms and Computation in Mathematics, 21. , Springer, Berlin
  • Luft, E., On 2-dimensional aspherical complexes and a problem of J.H.C. Whitehead (1996) Math. Proc. Camb. Phil. Soc, 119, pp. 493-495
  • May, J.P., Finite Topological Spaces (2003) Notes for REU, , http://www.math.uchicago.edu/~may/MISCMaster.html, Available at
  • McCord, M.C., Singular homology groups and homotopy groups of finite topological spaces (1966) Duke Math. J, 33, pp. 465-474
  • Stong, R.E., Finite topological spaces (1966) Trans. Am. Math. Soc, 123, pp. 325-340
  • Whitehead, J.H.C., On adding relations to homotopy groups (1941) Ann. Math, 42 (2), pp. 409-428

Citas:

---------- APA ----------
Cerdeiro, M.A. & Minian, E.G. (2014) . A new approach to Whitehead’s asphericity question. Journal of Homotopy and Related Structures, 9(2), 339-348.
http://dx.doi.org/10.1007/s40062-013-0031-x
---------- CHICAGO ----------
Cerdeiro, M.A., Minian, E.G. "A new approach to Whitehead’s asphericity question" . Journal of Homotopy and Related Structures 9, no. 2 (2014) : 339-348.
http://dx.doi.org/10.1007/s40062-013-0031-x
---------- MLA ----------
Cerdeiro, M.A., Minian, E.G. "A new approach to Whitehead’s asphericity question" . Journal of Homotopy and Related Structures, vol. 9, no. 2, 2014, pp. 339-348.
http://dx.doi.org/10.1007/s40062-013-0031-x
---------- VANCOUVER ----------
Cerdeiro, M.A., Minian, E.G. A new approach to Whitehead’s asphericity question. J. Homotopy Related Struct. 2014;9(2):339-348.
http://dx.doi.org/10.1007/s40062-013-0031-x