Generalized Property R and the Schoenflies Conjecture
نویسندگان
چکیده
منابع مشابه
On the Combinatorial Schoenflies Conjecture
Introduction. The combinatorial version of the Schoenflies conjecture in dimension n states: A combinatorial (n — l)-sphere on a combinatorial «-sphere decomposes the latter into two combinatorial ncells. The cases n = 1, 2 are obvious, the case n = 3 was solved by J. W. Alexander [l], see also W. Graeub [5], and E. Moise [8]. Nothing is known for n>3 (compare J. F. Hudson and E. C. Zeeman in [...
متن کاملThe generalized Schoenflies theorem
The generalized Schoenflies theorem asserts that if φ ∶ Sn−1 → S is a topological embedding and A is the closure of a component of Sn∖φ(Sn−1), then A ≅ D as long as A is a manifold. This was originally proved by Barry Mazur and Morton Brown using rather different techniques. We give both of these proofs.
متن کاملHandle Number One Links and Generalized Property R
It is shown that if the exterior of a 2-component link L in the three sphere admits a genus 2 Heegaard splitting, then L has Generalized Property R.
متن کاملOn Property (A) and the socle of the $f$-ring $Frm(mathcal{P}(mathbb R), L)$
For a frame $L$, consider the $f$-ring $ mathcal{F}_{mathcal P}L=Frm(mathcal{P}(mathbb R), L)$. In this paper, first we show that each minimal ideal of $ mathcal{F}_{mathcal P}L$ is a principal ideal generated by $f_a$, where $a$ is an atom of $L$. Then we show that if $L$ is an $mathcal{F}_{mathcal P}$-completely regular frame, then the socle of $ mathcal{F}_{mathcal P}L$ consists of those $f$...
متن کاملGeneralized Hopfian Property, Minimal Haken Manifold, and J. Simon’s Conjecture for 3-manifold Groups
We address a conjecture that π1-surjective maps between closed aspherical 3-manifolds having the same rank on π1 must be of non-zero degree. The conjecture is proved for Seifert manifolds, which is used in constructing the first known example of minimum Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3-manifolds. Section
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2008
ISSN: 0010-2571
DOI: 10.4171/cmh/131