We present a local combinatorial formula for the Euler class of an n-dimensional PL spherical fiber bundle as a rational number eCH associated to a chain of n + 1 abstract subdivisions of abstract n-spherical PL cell complexes. The number eCH is a combinatorial (or matrix) Hodgetheoretic twisting cochain in Guy Hirsch’s homology model of the bundle associated with the PL combinatorics of the bundle.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 507, 2021, pp. 35–58.
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Mnëv, N.E. A Note on a Local Combinatorial Formula for the Euler Class of a PL Spherical Fiber Bundle. J Math Sci 261, 614–629 (2022). https://doi.org/10.1007/s10958-022-05776-1
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DOI: https://doi.org/10.1007/s10958-022-05776-1