The paper introduces new invariants from weighted Betti numbers in triangulated manifolds.
problem Understanding invariants from weighted Betti numbers in triangulated manifolds.
method Introducing a new invariant defined as weighted averages of Betti numbers of induced subcomplexes, and proving its properties under operations on triangulated manifolds.
result The new invariants satisfy Alexander-Dehn-Sommerville type identities and have properties under operations on triangulated manifolds.