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Cell structures of simply-connected 5-manifolds (classified by Barden's 1965 paper)

In Barden's 1965 paper: Simply-connected five manifolds, Barden gave a complete list of diffeomorphism classes of simply-connected 5-manifolds: $$X_{j,k_1,\dots,k_n}=X_j\#M_{k_1}\#\cdots\#M_{k_n}$$ ...
Borromean's user avatar
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2 votes
0 answers
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Compare two topologies: Three 2-tori inside $S^3 \times S^1 \# S^2 \times S^2$ glued from two different diffeomorphisms

We like to ask for the comparison of two topologies of three 2-tori inside the same 4-manifolds glued from two different diffeomorphisms (see the end). Given an embedded torus $T$ with trivial normal ...
wonderich's user avatar
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1 vote
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Higher dimensional Seifert surfaces and link numbers of higher knots

In 3-manifold topology, the notion of Seifert surface is well known. It is then used to define link numbers of knots. Question: Consider embedding $N^n \rightarrow M^{2n+1}$ of n-dimensional manifold $...
0x11111's user avatar
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1 vote
0 answers
169 views

Confused about A. Kosinski's description about surgery in his book "differential manifolds"

Please excuse me, if MO is not the proper place for this question. I aksed the same question on M.SE https://math.stackexchange.com/questions/3511134/confused-about-a-kosinskis-description-of-surgery-...
Zest's user avatar
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1 vote
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76 views

Does a homotopy sphere that bounds a highly connected manifold also bound a parallelizable manifold?

Suppose that the homotopy sphere $\Sigma^{n}$ can be realized as the boundary of a smooth $(n+1)$-dimensional cobordism that is $(n-1)/2$-connected for $n$ odd (respectively, $(n-2)/2$-connected for $...
Rahmpilz's user avatar
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