One-relator groups and proper 3-realizability (2009)
Cárdenas, M., Lasheras, F. F., Quintero, A., Repovš, D.
How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group $G$ is said...
A new invariant of higher-dimensional embeddings (2008)
Cencelj, M., Repovš, D., Skopenkov, M.
This paper is on the classical Knotting Problem: for a given manifold N and a number m describe the set of isotopy classes of embeddings N->S^m. We study the specific case of knotted tori, i. e. the...
Characterizing compact Clifford semigroups that embed into convolution and functor-semigroups (2008)
Banakh, T., Cencelj, M., Hryniv, O., Repovš, D.
We study algebraic and topological properties of the convolution semigroups of probability measures on topological groups and show that a compact Clifford topological semigroup $S$ embeds into the...
Symmetric monochromatic subsets in colorings of the Lobachevsky plane (2008)
Banakh, T., Dudko, A., Repovš, D.
We prove that for each partition of the Lobachevsky plane into finitely many Borel pieces one of the cells of the partition contains an unbounded centrally symmetric subset.
Constructing near-embeddings of codimension one manifolds with countable dense singular sets (2008)
Repovš, D., Rosicki, W., Zastrow, A., Željko, M.
The purpose of this paper is to present, for all $n\ge 3$, very simple examples of continuous maps $f:M^{n-1} \to M^{n}$ from closed $(n-1)$-manifolds $M^{n-1}$ into closed $n$-manifold $M^n$ such...
Homotopy type of the complement of an immersion and classification of embeddings of tori (2008)
Cencelj, M., Repovš, D., Skopenkov, M.
This paper is devoted to the classification of embeddings of higher dimensional manifolds. We study the case of embeddings $S^p\times S^q\to S^m$, which we call knotted tori. The set of knotted tori...
Preserving $Z$-sets by Dranishnikov's resolution (2008)
Ageev, S. M., Cencelj, M., Repovš, D.
We prove that Dranishnikov's $k$-dimensional resolution $d_k\colon \mu^k\to Q$ is a UV$^{n-1}$-divider of Chigogidze's $k$-dimensional resolution $c_k$. This fact implies that $d_k^{-1}$ preserves...
On small homotopies of loops (2007)
Conner, G., Meilstrup, M., Repovš, D., Zastrow, A., Željko, M.
Two natural questions are answered in the negative: (1) If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops...
On $\pi - \pi$ theorem for manifold pairs with boundaries (2007)
Cencelj, M., Muranov, Yu. V., Repovš, D.
Surgery obstruction of a normal map to a simple Poincare pair $(X,Y)$ lies in the relative surgery obstruction group $L_*(\pi_1(Y)\to\pi_1(X))$. A well known result of Wall, the so called $\pi$-$\pi$...
On the fundamental group of $\mathbb R^3$ modulo the Case-Chamberlin continuum (2007)
Eda, K., Karimov, U. H., Repovš, D.
It has been known for a long time that the fundamental group of the quotient of $\RR ^3$ by the Case-Chamberlin continuum is nontrivial. In the present paper we prove that this group is in fact,...
Classification of framed links in 3-manifolds (2007)
Cencelj, M., Repovš, D., Skopenkov, M.
We present a short proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: {\bf Theorem.} Let $M$ be a connected oriented closed...
Amalgamated products and properly 3-realizable groups (2006)
Cardenas, M., Lasheras, F. F., Quintero, A., Repovš, D.
In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that $G$ is said to be properly...
On the splitting problem for manifold pairs with boundaries (2006)
Cencelj, M., Muranov, Yu. V., Repovš, D.
The problem of splitting a homotopy equivalence along a submanifold is closely related to the surgery exact sequence and to the problem of surgery of manifold pairs. In classical surgery theory there...
Surgery spectral sequence and stratified manifolds (2006)
Jimenez, R., Muranov, Yu. V., Repovš, D.
Cappell and Shaneson pointed out in 1978 interesting properties of Browder - Livesay invariants which are similar to differentials in some spectral sequence. Such spectral sequence was constructed in...
Splitting along a submanifold pair (2006)
Jimenez, R., Muranov, Yu. V., Repovš, D.
The paper introduces a group $LSP$ of obstructions for splitting a homotopy equivalence along a pair of submanifolds. We develop exact sequences relating the $LSP$-groups with various surgery...
Codimension two PL embeddings of spheres with nonstandard regular neighborhoods (2006)
Cencelj, M., Repovš, D., Skopenkov, A.
For a given polyhedron $K\subset M$ the notation $R_M(K)$ denotes a regular neighborhood of $K$ in $M$. We study the following problem: find all pairs $(m,k)$ such that if $K$ is a compact...