Prismatic Subdivision of a Simplicial Set in a Topological Sense

Year 2011, Volume: 3 Issue: 2, 76 - 89, 01.06.2011

B. Akyar

Abstract

We study prismatic sets which are very closely related to simplicial sets. The realization of a prismatic set leads us to
the prismatic subdivision of a simplicial set which is a special case of prismatic sets. We show the topological
relation between the prismatic subdivision of a simplicial set S and S itself and we give the nerve of this construction.

References

• B. Akyar, Lattice Gauge Field Theory, Phd. Thesis, Aarhus University, 2002.
• B. Akyar, J. L. Dupont, Lattice Gauge Field Theory and Prismatic Sets, Math. Scand., 1st issue, vol. 108, (2011).
• B. Akyar, Construction of Bundles on Simplicial sets and Transition functions, to appear in AJSE, G. E. Bredon, Topology and Geometry, GTM, Springer-Verlag New York, 1993.
• J. L. Dupont, R. Ljungmann, Integration of simplicial forms and Deligne Cohomology, Math. Scand., 96 (1), 2005, 11-39.
• D. Grayson, Exterior power operations on algebraic K-theory, K-Theory, 3, 1989, 247-260.
• Ju. T. Lisica, S. Mardešić, Coherent prohomotopy and strong shape theory, Glas. Mat. Ser. III (39), 1984, 335-399.
• S. Mac Lane, Homology, Grundlehren Math. Wiss., 114, Springer-Verlag, Berlin-G ottingen- Heidelberg, 1963.
• P. May, Simplicial Objects in Algebraic Topology, Chicago Lectures in Math., 1967.
• J. E. McClure, J. H. Smith, A solution of Deligne's Hochschild cohomology conjecture, Contemp. Math., 293, 2002, 153 - 193.
• J. Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math., 2, 1957, 357-362.
• A.V. Phillips, D.A. Stone, The Chern-Simons character of a lattice gauge field, Quantum Topology, , 244 - 291. G. Segal, Classifying spaces and spectral sequences, Publ. Math. I.H.E.S., 34, 1968, 105-112.