The topology of the independence complex

We introduce a large self-dual class of simplicial complexes for which we show that each member complex is contractible or homotopy equivalent to a sphere. Examples of complexes in this class include independence and dominance complexes of forests, pointed simplicial complexes, and their combinatorial Alexander duals.

[1]  Xun Dong,et al.  Alexander duality for projections of polytopes , 2002 .

[2]  Louis J. Billera,et al.  Decompositions of Partially Ordered Sets , 2000, Order.

[3]  Irene Gassko.  Stapled Sequences and Stapling Coverings of Natural Numbers , 1996, Electron. J. Comb..

[4]  Louis J. Billera,et al.  Shellability of Interval Orders , 1998 .

[5]  Michelle L. Wachs,et al.  Shellable nonpure complexes and posets. II , 1996 .

[6]  R. Stanley.  Combinatorics and commutative algebra , 1983 .

[7]  Martin Farber,et al.  Domination, independent domination, and duality in strongly chordal graphs , 1984, Discret. Appl. Math..

[8]  Dmitry N. Kozlov,et al.  Complexes of Directed Trees , 1999, J. Comb. Theory A.

[9]  Gil Kalai,et al.  Enumeration ofQ-acyclic simplicial complexes , 1983 .

[10]  Svante Linusson.  A Class of Lattices Whose Intervals are Spherical or Contractible , 1999, Eur. J. Comb..

[11]  Michael E. Saks,et al.  A topological approach to evasiveness , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[12]  Jeff Kahn,et al.  On lattices with M:obius function ±1, 0 , 1987, Discret. Comput. Geom..

[13]  Victor Reiner,et al.  Shifted simplicial complexes are Laplacian integral , 2002 .

[14]  Christina M. Mynhardt,et al.  Vertices contained in every minimum dominating set of a tree , 1999, J. Graph Theory.

[15]  Lonnie Athens.  ‘Domination’ , 2002 .

[16]  Charalambos A. Charalambides,et al.  Enumerative combinatorics , 2018, SIGA.

[17]  Marshall M. Cohen.  A Course in Simple-Homotopy Theory , 1973 .

[18]  Michael E. Saks,et al.  A topological approach to evasiveness , 1984, Comb..

[19]  Richard Ehrenborg,et al.  Playing Nim on a Simplicial Complex , 1996, Electron. J. Comb..

[20]  M. Wachs.  SHELLABLE NONPURE COMPLEXES AND POSETS , 1996 .