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Results tagged with gt.geometric-topology
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user 10839
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).
6
votes
Introduction to Floer Theory?
I wholeheartedly agree with both of Chris Gerig's suggestions.
The small McDuff-Salamon book on holomorphic curves ("J-holomorphic curves and quantum cohomology", available on McDuff's webpage) has a …
- 4,713
4
votes
Accepted
Path of almost complex structure in the definition of Heegaard Floer homology
According to Proposition 3.9 of Ozsvath and Szabo's original paper "Holomorphic disks and topological invariants for closed three-manifolds" there are indeed topological conditions one can put on the …
- 12.9k
7
votes
Books in advanced differential topology
As Deane Yang suggests, you could narrow down your task by picking a short paper and digging deep enough to understand all the ingredients that go into it. For this purpose, I can highly recommend Mil …
- 7,005
41
votes
Accepted
Why should I care about the Jones polynomial?
Your question presupposes that people were excited about the Jones polynomial because it would help them to classify/distinguish knots. In fact, I suspect the interest came from the fact that this kno …
- 7,005
5
votes
Symplectic Submanifolds of Contact Manifolds and Contact Submanifolds of Symplectic Manifolds
As Chris Gerig indicates in his comment, the correct notion is that of a contact-type hypersurface. These always exist, even locally. You could just take the boundary of a Darboux ball, which always e …
- 13.6k
17
votes
Intuitive crutches for higher dimensional thinking
One extremely useful trick for visualising a certain class of simple 4- and 6-dimensional spaces is the toric moment map picture.
(a) The basic example is a 2-sphere $\{x^2+y^2+z^2=1\}$, which you eq …
- 7,005
15
votes
Accepted
What prerequisites do I need to read the book Ricci Flow and the Poincare Conjecture, publis...
If I were going there I wouldn't start from here.
If you're new to 3-manifolds, it might better to familiarise yourself with them intimately before starting on Perelman's work. In fact, learning some …
- 7,005
11
votes
Accepted
book on calabi yau manifolds
Depending on how much of a beginner you are, you could begin by reading Barth-Hulek-Peters-Van de Ven paying particular attention to the section on K3 surfaces (which are 2-(complex)-dimensional Calab …
- 7,005