Related papers: Graphs of groups and the Atiyah conjecture for one…
We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for…
This article was withdrawn by the arXiv.org administrators since it plagiarizes math.GT/0011056.
We prove a Kunneth formula computing the Connes-Shlyakhtenko L^2-Betti numbers of the algebraic tensor product of two tracial *-algebras in terms of the L^2-Betti numbers of the two original algebras. As an application, we construct…
Paper withdrawn by the author.
This paper is removed from the network permanently. The content in this paper has now been put together with hep-th/9310183. See the recently replaced and widely revised version of the latter.
In this paper, we are motivated by two conjectures proposed by C. Bender et al.\ in 2024, which have remained open questions. The first conjecture states that if the complemented zero-divisor graph \( G(S) \) of a commutative semigroup \( S…
Green [Geometric and Functional Analysis 15 (2005), 340--376] established a version of the Szemer\'edi Regularity Lemma for abelian groups and derived the Removal Lemma for abelian groups as its corollary. We provide another proof of his…
This paper has been withdrawn due to a crucial error in the proof of the main theorem
This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.
This article is withdrawn because of a mistake in the main result of the paper.
In this paper we consider the asymptotic behavior of invariants such as Betti numbers, minimal numbers of generators of singular homology, the order of the torsion subgroup of singular homology, and torsion invariants. We will show that all…
This paper has been withdrawn by the author due to an error in the proof of Theorem 2.
this paper has been withdrawn. A crucial estimate on a Lipschitz variant of the Kakeya maximal function has an incomplete proof.
This paper has been withdrawn. See v1 still available to understand the problem: Proposition 2.2 is false. The error in the proof is in claim (3). Then, the whole paper collapses. We do not have any correction for now. We apologize to…
This is a part survey part research paper studying the local topology of complex analytic spaces. We review and strengthen the results of Kapovich--Koll\'ar "Fundamental groups of links of isolated singularities" (1109.4047) and incorporate…
This paper has been withdrawn due to an error, and no further revisions will be made.
This paper has been withdrawn by the author due to an error in the proof of Theorem 1.
Let $G$ be a countable group and $k$ a positive integer, we show that the $L^2$-Betti numbers of the group $G$ vanish up to degree $k$ provided that there is some infinite index subgroup $H$ with finite $k$th $L^2$-Betti number containing a…
This paper has been withdrawn because it is a duplicate of [math/0609208].
In this paper, we first prove a local family version of the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, then we extend the famous Witten's rigidity Theorems to the family case. Several family vanishing theorems for elliptic…