  We study the geometry and topology of exotic Springer fibers for orbits
corresponding to one-row bipartitions from an explicit, combinatorial point of
view. This includes a detailed analysis of the structure of the irreducible
components and their intersections as well as the construction of an explicit
affine paving. Moreover, we compute the ring structure of cohomology by
constructing a CW-complex homotopy equivalent to the exotic Springer fiber.
This homotopy equivalent space admits an action of the type C Weyl group
inducing Kato's original exotic Springer representation on cohomology. Our
results are described in terms of the diagrammatics of the one-boundary
Temperley-Lieb algebra (also known as the blob algebra). This provides a first
step in generalizing the geometric versions of Khovanov's arc algebra to the
exotic setting.
