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Journal of the London Mathematical Society (2)

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CONNECTED SUMS OF 4-MANIFOLDS AS CODIMENSION-k FIBRATORS
ROBERT J. DAVERMAN, YOUNG HO IM, YONGKUK KIM
Journal:

Journal of the London Mathematical Society / Volume 68 / Issue 1 / August 2003

Published online by Cambridge University Press:

08 August 2003, pp. 206-222

Print publication:

August 2003
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The main result provides mild conditions under which a closed, orientable, PL 4-manifold $N = N_1\,\#\,N_2$ with $\pi_1(N_e)$ residually finite ($e=1,2$) is a codimension-5 PL fibrator. The paper also presents a rich variety of conditions on a closed 4-manifold $N^4$ under which every PL map between manifolds, where the domain is orientable and all point inverses are copies of $N^4$, must be an approximate fibration.

CONNECTIONS AND CURVINGS ON LIFTING BUNDLE GERBES
KIYONORI GOMI
Journal:

Journal of the London Mathematical Society / Volume 67 / Issue 2 / April 2003

Published online by Cambridge University Press:

24 March 2003, pp. 510-526

Print publication:

April 2003
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A connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension are constructed. The construction is based on certain structures on the bundle, that is, connections and bundle splittings. The Deligne cohomology class of the lifting bundle gerbe with the connection and with the curving coincides with the obstruction class of the lifting problem with these structures.