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Community Bot
Community Bot
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Essentially the same question has been answered; see Generalizations of the handle trading techniquesGeneralizations of the handle trading techniques. For simply-connected manifolds, Smale showed that you can get a handle decomposition that is as simple as required by the homology groups. (The spin condition is not relevant at all.) A handle decomposition gives a homotopy equivalent cell complex; you won't get any simpler than this.

Essentially the same question has been answered; see Generalizations of the handle trading techniques. For simply-connected manifolds, Smale showed that you can get a handle decomposition that is as simple as required by the homology groups. (The spin condition is not relevant at all.) A handle decomposition gives a homotopy equivalent cell complex; you won't get any simpler than this.

Essentially the same question has been answered; see Generalizations of the handle trading techniques. For simply-connected manifolds, Smale showed that you can get a handle decomposition that is as simple as required by the homology groups. (The spin condition is not relevant at all.) A handle decomposition gives a homotopy equivalent cell complex; you won't get any simpler than this.

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Danny Ruberman
Danny Ruberman
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Essentially the same question has been answered; see Generalizations of the handle trading techniques. For simply-connected manifolds, Smale showed that you can get a handle decomposition that is as simple as required by the homology groups. (The spin condition is not relevant at all.) A handle decomposition gives a homotopy equivalent cell complex; you won't get any simpler than this.