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On the direct product conjecture for sigma invariants
Author(s) -
Schütz Dirk
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn048
Subject(s) - counterexample , conjecture , mathematics , direct product , product (mathematics) , pure mathematics , sigma , combinatorics , geometry , physics , quantum mechanics
We show that the direct product conjecture for Σ n ( G ; ℤ), where G is the direct product of two groups of type FP n , holds for n = 3 and give counterexamples for n ⩾ 4. Previously, counter‐examples were known only for a related conjecture involving the homotopical Σ‐invariants, where the conjecture already fails for n ⩾ 3.
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