Hybrid reduced and symmetric product spaces

AbstractWe show that, for any Tychonoff space X with base point θ, the infinite symmetric product SP∞ X of X is a subspace of an abelian group A(X) generated by X. (This clarifies the continuity of the multiplication in SP∞ X.) Furthermore, SP∞ X is a retract of A(X). Analogous results hold for reduced product spaces, with respect to non-abelian groups.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 99; secondary 54 B 15.

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Rank-one nonincreasing additive mappings on second symmetric product spaces

Linear Algebra and its Applications ◽

10.1016/j.laa.2005.01.002 ◽

2005 ◽

Vol 402 ◽

pp. 263-271 ◽

Cited By ~ 10

Author(s):

Ming-Huat Lim

Keyword(s):

Symmetric Product ◽

Product Spaces ◽

Rank One ◽

Additive Mappings

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GENERATING SERIES FOR SYMMETRIC PRODUCT SPACES

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887812500454 ◽

2012 ◽

Vol 09 (05) ◽

pp. 1250045 ◽

Cited By ~ 4

Author(s):

YONG SEUNG CHO

Keyword(s):

Projective Line ◽

Symmetric Product ◽

Product Spaces ◽

Topological Properties ◽

Geometric Invariants ◽

Generating Series ◽

Complex Projective Line ◽

Complex Projective

We consider the symmetric product spaces of closed manifolds. We introduce some geometric invariants and the topological properties of symmetric product spaces via the symmetric invariant ones of product spaces and apply to Gromov–Witten invariants. We examine the symmetric product spaces of the complex projective line, their Gromov–Witten invariants and compute the generating series induced by their Gromov–Witten invariants.

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On BP*(K(Z, 3); Z/p)

Canadian Journal of Mathematics ◽

10.4153/cjm-1983-036-3 ◽

1983 ◽

Vol 35 (4) ◽

pp. 630-653

Author(s):

Jack Ucci

Keyword(s):

Spectral Sequence ◽

Inverse Limit ◽

Explicit Description ◽

Symmetric Product ◽

Product Spaces

In this paper we study the inverse limit cohomology h*(K(Z, 3)) of an Eilenberg-MacLane object K(Z, 3) for certain cohomology theories h. Our main result gives a complete description of all non-trivial differentials of the Atiyah-Hirzebruch spectral sequence (AHSS) H*(X;h*(pt)) ⇒ h*(X) for X = K(Z, 3) and h either of the complex K-theories K*( ;Z/p) and K*( ;Z(p)). This is achieved inductively using the finite symmetric product spaces SPkS3, k = pr. Identification of cycles and boundaries of each non-trivial differential leads to an explicit description of BP<1>*(K(Z, 3); Z/p) and some information about BP<1>*(K(Z, 3)).

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