m at h . A T ] 2 4 Ju n 20 03 FIBER PRODUCTS , POINCARÉ DUALITY AND A ∞ - RING SPECTRA
نویسنده
چکیده
For a Poincaré duality space X and a map X → B, consider the homotopy fiber product X × X . If X is orientable with respect to a multiplicative cohomology theory E, then, after suitably regrading, it is shown that the E-homology of X × X has the structure of a graded associative algebra. When X → B is the diagonal map of a manifold X , one recovers a result of Chas and Sullivan about the homology of the unbased loop space LX .
منابع مشابه
ar X iv : m at h / 04 11 35 1 v 2 [ m at h . A T ] 1 7 N ov 2 00 4 POINCARÉ SUBMERSIONS
We prove two kinds of fibering theorems for maps X → P , where X and P are Poincaré spaces. The special case of P = S yields a Poincaré duality analogue of the fibering theorem of Browder and Levine.
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A few years ago, I defined a squarefree module over a polynomial ring S = k[x1, . . . , xn] generalizing the Stanley-Reisner ring k[∆] = S/I∆ of a simplicial complex ∆ ⊂ 2. This notion is very useful in the StanleyReisner ring theory. In this paper, from a squarefree S-module M , we construct the k-sheaf M on an (n − 1) simplex B which is the geometric realization of 2. For example, k[∆] is (th...
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A few years ago, I defined a squarefree module over a polynomial ring S = k[x1, . . . , xn] generalizing the Stanley-Reisner ring k[∆] = S/I∆ of a simplicial complex ∆ ⊂ 2. This notion is very useful in the StanleyReisner ring theory. In this paper, from a squarefree S-module M , we construct the k-sheaf M on an (n − 1) simplex B which is the geometric realization of 2. For example, k[∆] is (th...
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