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This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty of the approach is we rely heavily on the naturality of binary symmetric groups to avoid lengthy explicit constructions of smoothings of PL-manifolds.
For a field $mathbb{F}$, the notion of $mathbb{F}$-tightness of simplicial complexes was introduced by Kuhnel. Kuhnel and Lutz conjectured that any $mathbb{F}$-tight triangulation of a closed manifold is the most economic of all possible triangulatio
Combinatorial Ricci flow on a cusped $3$-manifold is an analogue of Chow-Luos combinatorial Ricci flow on surfaces and Luos combinatorial Ricci flow on compact $3$-manifolds with boundary for finding complete hyperbolic metrics on cusped $3$-manifold
Combinatorial Ricci flow on an ideally triangulated compact 3-manifold with boundary was introduced by Luo as a 3-dimensional analog of Chow-Luos combinatorial Ricci flow on a triangulated surface and conjectured to find algorithmically the complete
Discrete conformal structure on polyhedral surfaces is a discrete analogue of the smooth conformal structure on surfaces that assigns discrete metrics by scalar functions defined on vertices. In this paper, we introduce combinatorial $alpha$-curvatur
We derive the topological obstruction to spin-Klein cobordism. This result has implications for signature change in general relativity, and for the $N=2$ superstring.