Questions about surgery theory
(Difference between revisions)
(→Simply connected odd-dimensional L-groups) |
(→Simply connected surgery obstruction groups) |
||
Line 15: | Line 15: | ||
<wikitex>; | <wikitex>; | ||
How does one prove that | How does one prove that | ||
− | $L_{4j}(e)= | + | $L_{4j}(e)=\Zz$, $L_{4j+2}(e)=\Zz_2$, $L_{2k+1}(e) = 0$ ? |
Read {{cite|Kervaire&Milnor1963}} and/or {{cite|Browder1972}} and/or {{cite|Ranicki2002|Chapter 12}}. | Read {{cite|Kervaire&Milnor1963}} and/or {{cite|Browder1972}} and/or {{cite|Ranicki2002|Chapter 12}}. |
Revision as of 14:25, 13 August 2010
This page organizes questions and answers about surgery theory.
The natural first port of call for quick answers is Mathoverflow.
Below is a list of questions, possibly with answers.
The Atlas also has a chapter Questions for questions which attract longer answers.
Contents |
1 Questions
1.1 How can you tell if a space is homotopy equivalent to a manifold?
This is in fact a Mathoverflow question.
1.2 Simply connected surgery obstruction groups
How does one prove that , , ?
Read [Kervaire&Milnor1963] and/or [Browder1972] and/or [Ranicki2002, Chapter 12].
2 References
- [Browder1972] W. Browder, Surgery on simply-connected manifolds, Springer-Verlag, New York, 1972. MR0358813 (50 #11272) Zbl 0543.57003
- [Kervaire&Milnor1963] M. A. Kervaire and J. W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR0148075 (26 #5584) Zbl 0115.40505
- [Ranicki2002] A. Ranicki, Algebraic and geometric surgery, The Clarendon Press Oxford University Press, Oxford, 2002. MR2061749 (2005e:57075) Zbl 1003.57001