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104 votes
10 answers
24k views

Motivation for algebraic K-theory?

I'm looking for a big-picture treatment of algebraic K-theory and why it's important. I've seen various abstract definitions (Quillen's plus and Q constructions, some spectral constructions like ...
11 votes
2 answers
1k views

Elliptic curve over spectra?

Filling the gaps in my knowledge to understand the tmf question. So, what is the analogue of elliptic curve over the category of spectra?
Ilya Nikokoshev's user avatar
44 votes
7 answers
22k views

How do you show that $S^{\infty}$ is contractible?

Here I mean the version with all but finitely many components zero.
David Zureick-Brown's user avatar
11 votes
5 answers
3k views

Ribbon graph decomposition of the moduli space of curves

What is a ribbon graph? What is the ribbon graph decomposition of the moduli space of curves? What are some good references for this material?
Kevin H. Lin's user avatar
43 votes
5 answers
5k views

How can you tell if a space is homotopy equivalent to a manifold?

Is there some criterion for whether a space has the homotopy type of a closed manifold (smooth or topological)? Poincare duality is an obvious necessary condition, but it's almost certainly not ...
Eric Wofsey's user avatar
  • 31.2k
0 votes
0 answers
2k views

Ignore this question [closed]

This question is a hacky way to create some tags for you to use. Move along.
Anton Geraschenko's user avatar

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