分野別セミナー

Using ideas from theoretical physics as well as the concept of Eilenberg completeness of semirings from computer science, Markus Banagl has recently proposed the rigorous framework of so-called positive topological field theories (PTFTs). While capturing topological information in a state sum that obeys Atiyah’s gluing axiom, PTFTs have the potential to inspire the construction of innovative (differential) topological invariants for manifolds of arbitrary dimension.

In this talk, we explain Banagl’s construction of a concrete PTFT which extracts combinatorial data from the singular pattern of certain fold maps of bordisms into the plane. By eliminating the technical key condition Banagl imposes on fold maps, we attack the computation of the state sum. In particular, beyond a theorem of Saeki, we present our result on the detection of certain Kervaire spheres via indefinite folds.