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Homotopy theory, homological algebra, algebraic treatments of manifolds.

2 votes
0 answers
110 views

Generalized Cones

Let $K$ be a simplicial complex and $A$ be a subcomplex of $K$ such that $A$ is contractible. Suppose that for any simplex $\sigma\in K\setminus A$ and any vertex $v\in A$, $\sigma\cup \{v\}$ is a sim …
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203 views

Null-homotopicness of an inclusion map

Let $K$ and $L$ be simplicial complexes such that 1) $L\subseteq K$; 2) $K$ is homotopic to $S^4$; 3) $L$ is homotopic to $S^6$. Is the inclusion map from $L$ to $K$ null-homotopic? Thanks!
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