S. A. Melikhov

activity

20012026

most citedThe van Kampen obstruction and its relatives

33 citations · 154 across the 37 of their papers we have counts for

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Showing 2022Show all

5 papers · 1 filter

math.AT2022

Fine shape II: A Whitehead-type theorem

Sergey A. Melikhov

We prove an "abelian, locally compact" Whitehead theorem in fine shape: A fine shape morphism between locally connected finite-dimensional locally compact separable metrizable spac…

math.GT2022

Fine shape III: $Δ$ -spaces and $\nabla$ -spaces

Sergey A. Melikhov

In this paper we obtain results indicating that fine shape is tractable and "not too strong" even in the non-locally compact case, and can be used to better understand infinite-dim…

math.GT2022

Coronated polyhedra and coronated ANRs

Sergey A. Melikhov

Locally compact separable metrizable spaces are characterized among all metrizable spaces as those that admit a cofinal sequence $K_{1} \subset K_{2} \subset \dots$ of compact subsets. T…

math.GT2022

A triple-point Whitney trick

Sergey A. Melikhov

We use a triple-point version of the Whitney trick to show that ornaments of three orientable $(2 k - 1)$ -manifolds in $R^{3 k - 1}$ , $k > 2$ , are classified by the $μ$ -invariant.…

math.GT2022

Embeddability of joins and products of polyhedra

Sergey A. Melikhov

We present a short proof of S. Parsa's theorem that there exists a compact $n$ -polyhedron $P$ , $n \geq 2$ , non-embeddable in $R^{2 n}$ , such that $P * P$ embeds in $\mathbb R^{4…

Fine shape II: A Whitehead-type theorem

Fine shape III: Δ-spaces and ∇-spaces

Coronated polyhedra and coronated ANRs

A triple-point Whitney trick

Embeddability of joins and products of polyhedra

Fine shape III: $Δ$ -spaces and $\nabla$ -spaces