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20 votes
3 answers
2k views

Homotopy groups of spaces of embeddings

Let $\mathrm{Emb}(M, N)$ be the space of smooth embeddings of a closed manifold $M$ into a manifold $N$ equipped with smooth compact-open topology. Question 1. Are there conditions ensuring that ...
Igor Belegradek's user avatar
8 votes
0 answers
298 views

A conjecture about homotopy $S^1\times B^3$'s

$\textbf{Conjecture}:$ Let $X^4$ be a homotopy $S^1\times B^3$ with the following properties: Attaching a four dimensional 2-handle gives a standard $B^4$. The $k$-fold cyclic cover is diffeomorphic ...
Daniel H. Hartman's user avatar
4 votes
1 answer
220 views

Embedding spaces and surface knots in high dimensional manifolds

This is a variation of Craig's Knot complement diffeomorphism groups and embedding spaces for a different type of very simple manifold (surfaces which have a 1-relator fundamental group instead of ...
Nati's user avatar
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