E + B be a fiber bundle whose fiber Fis a compact smooth manifold, whose structure group G is a compact Lie group acting smoothly on F, and whose base B is a finite complex. Let x denote the Euler characteristic of F. It is shown in [12] that there exists a "transfer" homomorphism Q: H*(E) + H*(B) with the property that the composite @* is multiplication by II. The main purpose of this paper is to construct an Smap T: B+ + E+ which induces the homomorphism Q (+ denoting disjoint union with a base point). We call r the transfer associated with the fiber bundle p: E + B. In the case of a finite covering space T agrees with the transfer defined by Roush [22] and by Kahn and Priddy [18]. The existence of the transfer imposes strong conditions on the projection map of a fiber bundle. Specifically, we have the following THEOREM 5.7. Let 5 be a jiber bundle with fiber F having Euler characteristic x. Then p* @ 1: h*(B+) @Z[x-'1-h*(E+) @Z[x-'1 is a monomorphism onto a direct factor for anI> (reduced) cohomolog~ theory h. We will use the above theorem to establish a variant of the well known splitting principle for vector bundles (see Theorem 6.1). An application of this splitting principle is an alternative proof of the Adams conjecture (Quillen [21], Sullivan [25], Friedlander [ll]). The proof in outline is as follows. Theorem 6.1 asserts that if u is a 2n-dimensional real vector bundle over a finite complex Xthere exists a finite complex Y and amap%: Y + X such that (a) the structure group of i*(r) reduces to the normalizer N of a maximal torus in O(2n): (b) i*: /7*(X')-/I*(Y') is a monomorphism for any cohomology theory h. By (6.1) and the result of Boardman and Vogt [7] that BF. the classifying space for spherical fibrations is an infinite loop space. one is reduced to considering vector bundles with structure group N. An argument similar to the one employed by Quillen to treat vector bundles with finite structure group is then used to treat bundles of this form.

We have established early‐gestation chorionic villus–derived placenta mesenchymal stromal cells (PMSCs) as a potential treatment for spina bifida (SB), a neural tube defect. Our preclinical studies demonstrated that PMSCs have the potential to cure hind limb paralysis in the fetal lamb model of SB via a paracrine mechanism. PMSCs exhibit neuroprotective function by increasing cell number and neurites, as shown by indirect coculture and direct addition of PMSC‐conditioned medium to the staurosporine‐induced apoptotic human neuroblastoma cell line, SH‐SY5Y. PMSC‐conditioned medium suppressed caspase activity in apoptotic SH‐SY5Y cells, suggesting that PMSC secretome contributes to neuronal survival after injury. As a part of PMSC secretome, PMSC exosomes were isolated and extensively characterized; their addition to apoptotic SH‐SY5Y cells mediated an increase in neurites, suggesting that they exhibit neuroprotective function. Proteomic and RNA sequencing analysis revealed that PMSC exosomes contain several proteins and RNAs involved in neuronal survival and development. Galectin 1 was highly expressed on the surface of PMSCs and PMSC exosomes. Preincubation of exosomes with anti‐galectin 1 antibody decreased their neuroprotective effect, suggesting that PMSC exosomes likely impart their effect via binding of galectin 1 to cells. Future studies will include in‐depth analyses of the role of PMSC exosomes on neuroprotection and their clinical applications.—Kumar, P., Becker, J. C., Gao, K., Carney, R. P., Lankford, L., Keller, B. A., Herout, K., Lam, K. S., Farmer, D. L., Wang, A. Neuroprotective effect of placenta‐derived mesenchymal stromal cells: role of exosomes. FASEB J. 33, 5836–5849 (2019). http://www.fasebj.org

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