Continuum-wise injective maps

Injective Maps between Flip Graphs

We prove that every injective simplicial map F(S) → F(S′) between flip graphs is induced by a subsurface inclusion S → S′, except in finitely many cases. This extends a result of Korkmaz–Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is induced by a surface homeomorphism.

Injective Simplicial Maps of the Arc Complex

In this paper, we prove that each injective simplicial map of the arc complex of a compact, connected, orientable surface with nonempty boundary is induced by a homeomorphism of the surface. We deduce, from this result, that the group of automorphisms of the arc complex is naturally isomorphic to the extended mapping class group of the surface, provided the surface is not a disc, an annulus, a ...

The normal subsemigroups of the monoid of injective maps

We consider the monoid Inj(M) of injective self-maps of a set M and want to determine its normal subsemigroups by numerical invariants. This was established by Mesyan in 2012 if M is countable. Here we obtain an explicit description of all normal subsemigroups of Inj(M) for any uncountable set M .

There Are No Stable Points for Continuum-Wise Expansive Homeomorphisms

Indistinguishability Obfuscation from Trilinear Maps and Block-Wise Local PRGs

We consider the question of finding the lowest degree L for which L-linear maps suffice to obtain IO. The current state of the art (Lin, EUROCRYPT’16, CRYPTO ’17; Lin and Vaikunthanathan, FOCS’16; Ananth and Sahai, EUROCRYPT ’17) is that L-linear maps (under suitable security assumptions) suffice for IO, assuming the existence of pseudo-random generators (PRGs) with output locality L. However, ...