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Spaces of rational loops on a real projective space


Author: Jacob Mostovoy
Journal: Trans. Amer. Math. Soc. 353 (2001), 1959-1970
MSC (2000): Primary 26C15, 55P35
DOI: https://doi.org/10.1090/S0002-9947-01-02644-7
Published electronically: January 3, 2001
MathSciNet review: 1813601
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Abstract:

We show that the loop spaces on real projective spaces are topologically approximated by the spaces of rational maps $\mathbf{RP}^{1}\rightarrow \mathbf{RP}^{n}$. As a byproduct of our constructions we obtain an interpretation of the Kronecker characteristic (degree) of an ornament via particle spaces.


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Additional Information

Jacob Mostovoy
Affiliation: Instituto de Matemáticas (Unidad Cuernavaca), Universidad Nacional Autónoma de México, A.P. 273-3, C.P. 62251, Cuernavaca, Morelos, México
Email: jacob@matcuer.unam.mx

DOI: https://doi.org/10.1090/S0002-9947-01-02644-7
Keywords: Loop space, rational map, ornament, Kronecker characteristic
Received by editor(s): June 2, 1998
Received by editor(s) in revised form: October 18, 1999
Published electronically: January 3, 2001
Article copyright: © Copyright 2001 American Mathematical Society