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Homotopy type of mapping spaces and existence of geometric exponents
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Jaka Smrekar
Published/Copyright:
February 8, 2010
Abstract
Let Y be a simply connected finite complex and let p be a prime. Let Sm[p–1] denote the complex obtained from the m-sphere by inverting p. It is shown in this paper that Y has an eventual H-space exponent at p if and only if the space map*(Sm[p–1], Y) of pointed maps Sm[p–1] → Y has the homotopy type of a CW complex for some (and hence all big enough) m. This makes it possible to interpret the question of eventual H-space exponents in terms of phantom phenomena of mapping spaces.
Received: 2008-02-24
Revised: 2008-07-21
Published Online: 2010-02-08
Published in Print: 2010-May
© de Gruyter 2010
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Articles in the same Issue
- Brill-Noether theory for moduli spaces of sheaves on algebraic varieties
- Homotopy type of mapping spaces and existence of geometric exponents
- Extension theorems for spheres in the finite field setting
- Accessible subcategories of modules and pathological objects
- Characteristic cohomotopy classes for families of 4-manifolds
- Generators of simple Lie algebras II
- L1-determined ideals in group algebras of exponential Lie groups
- Simple mass formulas on Shimura varieties of PEL-type
- Uniqueness for elliptic operators on with unbounded coefficients
- Homogeneous principal bundles and stability
