SB-labelings and posets with each interval homotopy equivalent to a   sphere or a ball
  We introduce a new class of poset edge labelings for locally finite lattices which we call $SB$-labelings. We prove for finite lattices which admit an $SB$-labeling that each open interval has the homotopy type of a ball or of a sphere of some dimension. Natural examples include the weak order, the Tamari lattice, and the finite distributive lattices. 
Patricia Hersh and Karola Meszaros
math.CO math.AT