Is there any sort of Kneser Milnor decomposition in dimension d larger than or equal to 4?, I mean a family of d1 dimensional spheres disconnecting the ddimensional manifold into irreducible components and with some uniqueness?, If so, any reference so far?. Thanks.

Some results are available in dimension 4, although a "complete" answer is not known. As expected, the known results depend on the category: smooth/topological. Here are some references: first two papers by Matthias Kreck, Wolfgang Lück and Peter Teichner: "Counterexamples to the Kneser conjecture in dimension four", Comment. Math. Helv. 70 (1995), 423–433. "Stable prime decompositions of fourmanifolds". Prospects in topology, 251–269, Ann. of Math. Stud., 138, Princeton Univ. Press, Princeton, NJ, 1995. The first paper gives various counterexamples to the "naive" guess for 4dimensional Kneser's conjecture: that a free product decomposition of the fundamental group would lead to a connected sum decomposition. The second paper gives a proof of this "naive" prime decomposition theorem (including uniqueness) stably, i.e. up to a connected sum with copies of $S^2\times S^2$. (The existence of such a stable decomposition is also proved by Jonathan Hillman, "Free products and 4dimensional connected sums" Bull. London Math. Soc. 27 (1995), 387–391.) Some further results are known in the topological category, these hold up to scobordism (given that topological surgery and scobordism conjectures are not known for "large" fundamental groups, at this point one doesn't expect an actual result up to a homeomorphism). These theorems are of the following flavor: under some restrictions assume the fundamental group splits as a free product and also assume the second homotopy group and the intersection pairing "look like" they correspond to a connected sum decomposition (these are natural algebraic assumptions).Then up to an scobordism the manifold splits as a connected sum. Some of the references are: A. Cavicchioli, F. Hegenbarth, On 4manifolds with free fundamental group, Forum Math. 6 (1994), 415429; V. Krushkal, R. Lee, Surgery on closed 4manifolds with free fundamental group, Math. Proc. Cambridge Philos. Soc. 133 (2002), 305–310; Q. Khan, Homotopy invariance of 4manifold decompositions: connected sums, arXiv:0907.0308 

