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Questions tagged [homology]

Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.

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Topology of connected subsets of the $3$-torus

Consider the $3$-torus $Y=T^3$, a subset $\Sigma\subset Y$, and $\Sigma^*=Y\setminus\overline\Sigma$. We assume both $\Sigma$ and $\Sigma^*$ to be open, connected, and smoothly bounded. I am ...
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map of inductive systems of distinguished triangles

I have for any $n$ some distinguished triangles $$X_n->Y_n->Z_n$$ $$X'_n->Y'_n->Z'_n$$ The families $(X_n), (Y_n), (X'_n), (Y'_n)$ are inductive systems, $(X_n)$ is quasi-isomorphic to $(X'...