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math.CO2010
A counterexample to Wegner's conjecture on good covers
Martin Tancer
In 1975 Wegner conjectured that the nerve of every finite good cover in R^d is d-collapsible. We disprove this conjecture. A good cover is a collection of open sets in R^d such tha…
math.CO2010
A geometric proof of the colored Tverberg theorem
Jiří Matoušek, Martin Tancer, Uli Wagner
The colored Tverberg theorem asserts that for every d and r there exists t=t(d,r) such that for every set C in R^d of cardinality (d+1)t, partitioned into t-point subsets C_1,C_2,.…