A FIXED POINT THEOREM AND RELATIVE ASPHERICITY by Max FORESTER and Colin ROURKE
نویسندگان
چکیده
We give short new geometric proofs of theorems of Bogley and Pride and of Serre. Both follow quickly from a global fixed point theorem. The Bogley–Pride theorem concerns aspherical relative group presentations and was applied in [5] to the multivariable adjunction problem. Serre’s theorem is a basic result concerning group cohomology and finite subgroups.
منابع مشابه
The adjunction problem and a theorem of Serre
In this note we prove injectivity and relative asphericity for “layered” systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. We also give elementary geometric proofs of results due to Bogley–Pride and Serre that are used in the proof of the main theorem. AMS Classification 20E22, 20F05; 57M20, 57Q05
متن کامل4 The adjunction problem over torsion - free groups
In this note we prove injectivity and relative asphericity for “layered” systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. We also give an elementary geometric proof of a result due to Bogley–Pride and Serre that is used in the proof of the main theorem. AMS Classification 20E22, 20F05; 57M20, 57Q05
متن کاملMarkov's theorem in 3{manifolds
Sofia Lambropoulou and Colin Rourke Abstract In this paper we rst give a one-move version of Markov's braid theorem for knot isotopy in S3 that sharpens the classical theorem. Then a relative version of Markov's theorem concerning a xed braided portion in the knot. We also prove an analogue of Markov's theorem for knot isotopy in knot complements. Finally we extend this last result to prove a M...
متن کاملOn the Residual Finiteness and Other Properties of (relative) One-relator Groups
A relative one-relator presentation has the form P = 〈x,H;R〉 where x is a set, H is a group, and R is a word on x±1 ∪H. We show that if the word on x±1 obtained from R by deleting all the terms from H has what we call the unique max-min property, then the group defined by P is residually finite if and only if H is residually finite (Theorem 1). We apply this to obtain new results concerning the...
متن کامل2 6 M ay 2 00 4 Markov ’ s theorem in 3 – manifolds
In this paper we first give a one-move version of Markov’s braid theorem for knot isotopy in S that sharpens the classical theorem. Then a relative version of Markov’s theorem concerning a fixed braided portion in the knot. We also prove an analogue of Markov’s theorem for knot isotopy in knot complements. Finally we extend this last result to prove a Markov theorem for links in an arbitrary or...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005