33 citations · 327 across the 34 of their papers we have counts for
34 papers
The Chang-Skjelbred lemma and generalizations
Matthias Franz
We review the Chang-Skjelbred lemma for torus-equivariant cohomology and discuss several generalizations of it: to other coefficients, other groups and also to syzygies in equivari…
Cohomology of smooth toric varieties: naturality
Matthias Franz, Xin Fu
Building on the recent computation of the cohomology rings of smooth toric varieties and partial quotients of moment-angle complexes, we investigate the naturality properties of th…
The cohomology rings of real toric spaces and smooth real toric varieties
Matthias Franz
We compute the cohomology rings of smooth real toric varieties and of real toric spaces, which are quotients of real moment-angle complexes by freely acting subgroups of the ambien…
Szczarba's twisting cochain is comultiplicative
Matthias Franz
We prove that Szczarba's twisting cochain is comultiplicative. In particular, the induced map from the cobar construction of the chains on a 1-reduced simplicial set X to the chain…
Syzygies in equivariant cohomology in positive characteristic
Christopher Allday, Matthias Franz, Volker Puppe
We develop a theory of syzygies in equivariant cohomology for tori as well as -tori and coefficients in . A noteworthy feature is a new algebraic approach to the p…
Szczarba's twisting cochain and the Eilenberg-Zilber maps
Matthias Franz
We show that Szczarba's twisting cochain for a twisted Cartesian product is essentially the same as the one constructed by Shih. More precisely, Szczarba's twisting cochain can be…