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The Quarterly Journal of Mathematics 2001 52(2):249-259; doi:10.1093/qjmath/52.2.249
© 2001 by Oxford University Press
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Spaces of Holomorphic Maps with Bounded Multiplicity

Kohhei Yamaguchi1

1 University of Electro-Communications, Chofu, Tokyo 182-8585, Japan. E-mail: kohhei@im.uec.ac.jp

Let Hold* (S2, CPn–1) be the space consisting of all basepoint preserving holomorphic maps f : S2 -> CPn–1 of degree d. Then it is homeomorphic to the n-tuples (p1(z), ..., pn(z)) C[z]n of monic polynomials of degree d with no common root. Segal proved that it is a finite-dimensional model of {Omega}2 CPn–1. In this paper, we consider a certain subspace of it defined using the concept of multiplicity of roots, and we prove that it is also a finite-dimensional model of certain double loop space.


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