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According to the paper ``Heterotic and Type I String Dynamics from Eleven Dimensions'' (page 7):

Even when the topology is wrong -- for instance on $\mathbb{R}^{11}$ where there is no two-cycle for the membrane to wrap around -- macroscopic membrane solutions (with a scale much bigger than the Planck scale) will make sense, but we do not assume they can be quantized to recover gravitons.

This seems like a result from basic topology that I ought to know. But in general, how do I know whether there is a $k$-cycle for a membrane to wrap around a given manifold $\mathcal{M}$?

In this particular case, is it just that $\mathbb{R}^{11}$ has genus 0, and hence not even a one cycle to wrap around?

Possibly related thread which does not answer my question: What does it mean to "wrap" a D-brane around some manifold?

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