On Time-Reversal Equivariant Hermitian Operator Valued Maps from a 2D-Torus Phase Space
In this paper we classify maps from a torus phase space $X$ to $\mathcal{H}_n^*$, the space of $n \times n$, non-singular hermitian operators up to equivariant homotopy. The equivariance is with respect to a time-reversal involution on $X$ and an involution on $\mathcal{H}_n^*$ defining a certain symmetry class. Furthermore we study certain controlled degenerations of such maps and describe how one can implement jumps from one homotopy class to another while allowing only "small" degenerations.
math.GT↗