Gravitational sources induced by exotic smoothness and fermions as knot complements

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In this paper we will discuss Brans conjecture that exotic smoothness serves as an additional gravitational source naturally arising from the handlebody construction of the exotic R⁴. We will consider the two possible classes, the large and the small exotic R⁴. Then we calculate the Einstein-Hilbert action for both exotic R⁴ to show the apearance of spinor fields. Then we discuss the physical properties of these spinor fields to relate them to fermions. Finally we identify the corresponding 3-manifolds as knot complements of hyperbolic knots, i.e. the knot complements are hyperbolic 3-manifolds with finite volume. With the help of this result we confirm the Brans conjecture for both kinds of exotic R⁴.