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Results tagged with at.algebraic-topology
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user 10839
Homotopy theory, homological algebra, algebraic treatments of manifolds.
1
vote
Accepted
Homeomorphism between base of conifolds and spheres
Your space X is $\mathbf{RP}^3$. To see this, blow-up the origin. The proper transform of Y is then the total space of the bundle $\mathcal{O}(-2)\to\mathbf{CP}^1$. The unit circle bundle (your space …
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7
votes
Other Homology Theories still Count Holes?
Symplectic homology of the cotangent bundle is the homology of loop space (see Viterbo's "Functors and computations in Floer homology" or Abbondandolo-Schwartz).
Also, Cohen-Jones-Segal have a paper …
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8
votes
Motivation of the fundamental theorem of covering spaces
Many results in algebraic topology are proved using an argument along the following lines. Suppose such and such holds. Then there is a subgroup of the fundamental group with the following properties. …
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4
votes
Coincidences amongst classifying spaces and Eilenberg Mac-Lane spaces
This is not really an answer to the question posed but seems to be of relevance to people interested in the question (and is directly related to the case $BSU(2)\cong_{\mathbb{Q}}K(\mathbb{Z},4)$ ment …
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15
votes
1
answer
830
views
Nonisotopic homotopy equivalent Morse functions
One can cut a manifold up along the critical levels of a Morse function and deduce something about the topology. In particular the critical points (and the connecting gradient flowlines) define a chai …
- 7,005
4
votes
Accepted
Are Lefschetz thimbles holomorphic manifolds?
If by holomorphic manifold you mean that it happens to be a complex manifold then the answer is surely "not always", because in the case when the total space is $\mathbf{C}^3$ and the function is $(z_ …
- 7,005
9
votes
Accepted
Del Pezzo surfaces and Picard-Lefschetz theory
Indeed you can see it this way. This is my symplectic geometer's
perspective on it (I blame Paul Seidel's Lecture notes on four-dimensional Dehn twists).
Consider the $n$-point blow-up of $\mathbf{CP …
- 7,005
7
votes
Link of a singularity
To add to the excellent answers already provided, here are some general facts in the case of rational surface singularities (1 and 2) and hypersurface singularities (3).
Many interesting singulariti …
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