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Kervaire-Laudenbach Conjecture

1.
Systems of equations over locally p-indicable groups, Invent. Math. 81 (1985), 373-378.



SUMMARY:


I spent three terms in Toronto, studying under McCool's guidance. Most of my resesarch time was devoted to the Kervaire-Laudenbach Conjecture. Howie's ``locally indicable'' paper [H] was the inspiration. I was trying hard to prove the conjecture for locally non-perfect groups; that happenned to be too difficult, not just for me, but for the others working in the area at the time as well. I gave up, like everybody else, and published the article [1], which contains an algebraic version of Howie's proof, and also a stronger result using the p-adic completions of free groups. Similar results were proved by Gersten [G] and Stallings [S].



REFERENCES:


[G]
S. M. Gersten, Conservative groups, indicability and a conjecture of Howie, J. Pure Appl. Algebra 29 (1983), 59-74.

[H]
J. Howie, On pairs of 2-complexes and systems of equations over groups, J. Reine Angew. Math. 324 (1981), 445-461.

[S]
J. R. Stallings, Surfaces in three-manifolds and non-singular equations in groups, Math. Z. 184 (1983), 1-17.


next up previous
Next: Reactions to proofs of Up: SUMMARY OF RESULTS Previous: Automorphisms of free G-groups

2000-03-16