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- W2980492408 abstract "Deciding whether two simplicial complexes are homotopy equivalent is a fundamental problem in topology, which is famously undecidable. There exists a combinatorial refinement of this concept, called simple-homotopy equivalence: two simplicial complexes are of the same simple-homotopy type if they can be transformed into each other by a sequence of two basic homotopy equivalences, an elementary collapse and its inverse, an elementary expansion. In this article we consider the following related problem: given a 2-dimensional simplicial complex, is there a simple-homotopy equivalence to a 1-dimensional simplicial complex using at most p expansions? We show that the problem, which we call the erasability expansion height, is W[P]-complete in the natural parameter p." @default.
- W2980492408 created "2019-10-25" @default.
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- W2980492408 date "2019-10-21" @default.
- W2980492408 modified "2023-09-26" @default.
- W2980492408 title "Parametrized Complexity of Expansion Height" @default.
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- W2980492408 doi "https://doi.org/10.4230/lipics.esa.2019.13" @default.
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