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- W4315588730 abstract "For an integer $rge 2$, the space of $r$-immersions of $M$ in $mathbb R^n$ is defined to be the space of immersions of $M$ in $mathbb R^n$ such that at most $r-1$ points of $M$ are mapped to the same point in $mathbb R^n$. The space of $r$-immersions lies between the embeddings and the immersions. We calculate the connectivity of the layers in the homological Taylor tower for the space of $r$-immersions in $mathbb R^n$ (modulo immersions), and give conditions that guarantee that the connectivity of the maps in the tower approaches infinity as one goes up the tower. We also compare the homological tower with the homotopical tower, and show that up to degree $2r-1$ there is a Hurewicz isomorphism between the first non-trivial homotopy groups of the layers of the two towers." @default.
- W4315588730 created "2023-01-11" @default.
- W4315588730 creator A5033114211 @default.
- W4315588730 creator A5071227826 @default.
- W4315588730 date "2023-01-08" @default.
- W4315588730 modified "2023-09-27" @default.
- W4315588730 title "Intrinsic convergence of the homological Taylor tower for $r$-immersions in $mathbb R^n$" @default.
- W4315588730 doi "https://doi.org/10.48550/arxiv.2301.03131" @default.
- W4315588730 hasPublicationYear "2023" @default.
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