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Results tagged with gt.geometric-topology
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user 4991
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
3
votes
0
answers
106
views
Using blow-up for handle attachment
In basic surgery theory, it is clear what happens topologically when one "adds a handle", but getting the smooth structure right requires care. For example, in identifying opposite sides of a rectang …
- 4,990
7
votes
$\pi_4$ of simply-connected 4-manifold
First an important distinction: "Each element in $\pi_3(\vee S^2)$ has description in terms of linking number of point preimages (circles in $S^3$) of map $S^3 \to S^2$" is not a fully correct stateme …
- 4,990
2
votes
Accepted
Intersection map giving rise to Poincaré duality
In a related and highly relevant comment thread, Mike Miller pointed me to this preprint of Lipyanskiy. I'm sure there are arguments which work, such as what Joshua and Dmitri and I discuss in the co …
- 4,990
11
votes
1
answer
472
views
Intersection map giving rise to Poincaré duality
Let $M$ be a smoothly triangulated compact $d$-dimensional manifold. Consider the subcomplex $C_*^{\pitchfork T}(M)$ of smooth singular chains which are transverse to the triangulation. An inductive …
- 4,990
2
votes
Rational homotopy type of a complement
Some of the best results known along these lines are in the paper
Pascal Lambrechts, Don Stanley, Algebraic models of Poincaré embeddings, Algebr. Geom. Topol. 5 (2005) 135-182, doi:10.2140/agt.2005. …
- 4,990