Contractible, non-collapsible products with cubes

Knots in Collapsible and Non-Collapsible Balls

We construct the first explicit example of a simplicial 3-ball B15,66 that is not collapsible. It has only 15 vertices. We exhibit a second 3-ball B12,38 with 12 vertices that is collapsible and not shellable, but evasive. Finally, we present the first explicit triangulation of a 3-sphere S18,125 (with only 18 vertices) that is not locally constructible. All these examples are based on knotted ...

Cartesian Products of Contractible Open Manifolds

Mitigating Non-contractible Actions by Randomness

This paper studies non-contractibility of a contract designer's actions in an agency model with costly monitoring. It shows that non-contractibility may lead to an explicit randomness, which is not optimal under full contractibility. The randomness mitigates non-contractibility. Its e ectiveness increases with the ex post deducibility of the non-contractible variable. Mitigation is perfect, if ...

Floer Cohomology and Non - Contractible Periodic Orbits

For a closed symplectic manifold (M,ω), a compatible almost complex structure J , a 1-periodic time dependent symplectic vector field Z and a homotopy class of closed curves γ we define a Floer complex based on 1-periodic trajectories of Z in the homotopy class γ. We show how to associate to the above data an invariant, the symplectic torsion, which is an element in the Whitehead group Wh(Λ0), ...

Efficient Non-Contractible Investments in Large Economies

Do investors making complementary investments face the correct incen­ tives, especially when they cannot contract with each other prior to their de­ cisions? We present a two-sided matching model in which buyers and sellers make investments prior to matching. Once matched, buyer and seller bar­ gain over the price, taking into account outside options. Efficient decisions can always be sustained...