Finiteness in the minimal models of Sullivan

Stephen Halperin
1977 Transactions of the American Mathematical Society  
Let A" be a 1-connected topological space such that the vector spaces n^A") ® Q and H*(X; Q) are finite dimensional. Then H*(X\ Q) satisfies Poincaré duality. Set xn = 2(-lydim Up{X) ® Q and Xr " 2(-lydim HP(X; Q). Then Xn < 0 and & > 0. Moreover the conditions: (1) Xn = 0, (2) Xc > 0, H*(X; Q) evenly graded, are equivalent. In this case H*(X; Q) is a polynomial algebra truncated by a Borel ideal. Finally, if A" is a finite 1-connected C.W. complex, and an /--torus acts continuously on X with
more » ... nuously on X with only finite isotropy, then xn < -r-
doi:10.1090/s0002-9947-1977-0461508-8 fatcat:3yrltxjjifgzdbewjvgjnbx36a