Spaces of rational loops on a real projective space

Mostovoy, Jacob

doi:10.1090/s0002-9947-01-02644-7

Cited by 18 publications

(7 citation statements)

References 17 publications

(33 reference statements)

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“…A very general conjecture on this subject is given in the paper of Cohen, Jones and Segal [3]. Several papers [12,17] give real versions of Segal's theorem (the first real version being due to Segal himself in [20]).…”

Section: Introductionmentioning

confidence: 99%

Spaces of Morphisms From a Projective Space to a Toric Variety

Mostovoy¹,

Munguia-Villanueva²

2014

Revista Colombiana de Matemáticas

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In this paper we study the space of morphisms from a complex projective space to a compact smooth toric variety X. It is shown that the first author's stability theorem for the spaces of rational maps from CP m to CP n extends to the spaces of continuous morphisms from CP m to X essentially, with the same proof. In the case of curves, our result improves the known bounds for the stabilization dimension.2010 Mathematics Subject Classification. Primary: 58D15; Secondary: 32Q55.

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Section: Introductionmentioning

confidence: 99%

Spaces of Morphisms From a Projective Space to a Toric Variety

Mostovoy¹,

Munguia-Villanueva²

2014

Revista Colombiana de Matemáticas

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“…Another situation which has been extensively studied is the case when X and Y are compact complex manifolds and X has dimension one. Segal in [11] proved, among other things, that the inclusion of the space of (based) rational maps of degree d from CP 1 to CP n into the two-fold loop space of CP n is a homotopy equivalence up to dimension (2n − 1)d. The results of [11] were later extended by various authors: see, for example [1], [4], [5], [7], [8]. In all these generalizations X is a curve.…”

Section: Introductionmentioning

confidence: 92%

Spaces of rational maps and the Stone–Weierstrass theorem

Mostovoy

2006

Topology

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“…[2]). Although it has been sometimes stated that these phenomena are inherently related to complex or at least symplectic structures, real analogs of Segal's result were given in [13], [10], [7], [15]. In fact, Segal formulated the complex and real approximation theorems which he had proved as a single statement involving equivariant equivalence, with respect to complex conjugation (see the remark after Proposition 1.4 of [13]).…”

Section: Introductionmentioning

confidence: 99%

Spaces of algebraic maps from real projective spaces into complex projective spaces

Kozłowski

Yamaguchi²

2010

Homotopy Theory of Function Spaces and Related Topics

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We study the homotopy types of certain spaces closely related to the spaces of algebraic (rational) maps from the m dimensional real projective space into the n dimensional complex projective space for 2 ≤ m ≤ 2n (we conjecture this relation to be a homotopy equivalence).In [9] we proved that natural maps of these spaces to the spaces of all continuous maps are Z/2-equivariant homotopy equivalences, where the Z/2-equivariant action is induced from the conjugation on C. In the same article we also proved that the homotopy types of the terms of the natural degree filtration approximate closer and closer the homotopy type of the space of continuous maps and obtained bounds that describe the closeness of the approximation in terms of the degrees of the maps. In this paper, we improve the estimates of the bounds by using new methods invented in [13] and used in [10].In addition, in the the last section, we prove a special case (m = 1) of the conjecture stated in [1] that our spaces are homotopy equivalent to the spaces of algebraic maps.

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Spaces of rational loops on a real projective space

Abstract: Abstract. We show that the loop spaces on real projective spaces are topologically approximated by the spaces of rational maps RP 1 → RP n . As a byproduct of our constructions we obtain an interpretation of the Kronecker characteristic (degree) of an ornament via particle spaces.

Cited by 18 publications

References 17 publications

Spaces of Morphisms From a Projective Space to a Toric Variety

Spaces of Morphisms From a Projective Space to a Toric Variety

Spaces of rational maps and the Stone–Weierstrass theorem

Spaces of algebraic maps from real projective spaces into complex projective spaces

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