and

**Theorem 5.** *Let e be an exotic* **R**<sup>4</sup> *corresponding to the codimension-1 foliation of S*<sup>3</sup> *which gives rise to the C*�*algebra* <sup>A</sup>*e. The exotic smooth* **<sup>R</sup>**<sup>4</sup> *embedded in e determines a generalized quantum D-brane in* A*e.*

It is interesting to note that the tame subspace interpretation of D-branes can be recovered for the special class of the topological quantum D-branes. However, the embedding is replaced now by the wild embedding into spacetime, which historically appeared in the description of the horned Alexander's spheres, known from topology.

**Theorem 6.** *Let* **R**<sup>4</sup> *<sup>H</sup> be some exotic* **<sup>R</sup>**<sup>4</sup> *determined by element in H*3(*S*3, **<sup>R</sup>**)*, i.e. by a codimension-1 foliation of S*3*. Each wild embedding i* : *<sup>K</sup>*<sup>3</sup> <sup>→</sup> *<sup>S</sup><sup>p</sup> for p* <sup>&</sup>gt; <sup>6</sup> *of a 3-dimensional polyhedron determines a class in Hn*(*Sn*, **<sup>R</sup>**) *which represents a wild embedding i* : *<sup>K</sup><sup>p</sup>* <sup>→</sup> *<sup>S</sup><sup>n</sup> of a p -polyhedron into Sn.*

Now, a class of *topological quantum Dp-branes* are these branes which are determined by the wild embeddings *<sup>i</sup>* : *<sup>K</sup><sup>p</sup>* <sup>→</sup> *<sup>S</sup><sup>n</sup>* as above and in the classical and flat limit correspond to tame embeddings. In fact, *B*-field on *S*<sup>3</sup> can be translated into wild embeddings of higher dimensional objects and generates quantum character of these branes.
