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Misha

UC Davis

http://www.math.ucdavis.edu/~kapovich

My research area is geometric geometry, geometric topology and geometric group theory. Occasionally, I apply these to other fields, like algebraic geometry and representation theory.
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Top Questions
Top Answers
95
What is the difference between holonomy and monodromy?
mathoverflow.net

50
Does the curvature determine the metric?
mathoverflow.net

40
What is the Krull dimension of the ring of holomorphic functions on a complex manifold?
mathoverflow.net

40
Understanding groups that are not linear
mathoverflow.net

40
Does the moduli space of smooth curves of genus g contain an elliptic curve
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40
What are some examples of ingenious, unexpected constructions?
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38
Why is the fundamental group of a compact Riemann surface not free ?
mathoverflow.net

36
Can the holomorphic image of $(\mathbb{C}^*)^n$ be open but not dense
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34
Proofs of the Stallings-Swan theorem
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34
Does a *topological* manifold have an exhaustion by compact submanifolds with boundary?
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28
Well known theorems that have not been proved
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26
Surfaces filled densely by a geodesic
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26
Are all free groups linear, i.e., admit a faithful representation to GL(n,K) for some field K ?
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25
Are topological manifolds homotopy equivalent to smooth manifolds?
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25
Two commuting mappings in the disk
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19
Diffeomorphisms of finite order not in the image of a circle action
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19
Are congruence subgroups of the modular group finitely presented?
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19
Proper discontinuity and existence of a fundamental domain
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17
Is there any progress on Problem 12 (from Schoen and Yau)?
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16
Quote by Thurston on the Ricci flow
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16
Is there an algebraic approach to metric spaces?
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16
What is the geometry of an undecidable diophantine equation?
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16
Finite index free subgroups of $\mathrm{SL}(3,\mathbb{Z})$
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16
Can the group of holomorphic automorphisms of an open subset of the complex plane be isomorphic to the additive group of real numbers?
mathoverflow.net

16
Mathematics of quasicrystals
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16
quasi-homomorphisms of groups
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15
Determine if you can build a polygon from segments
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15
Can the SL_2 character variety of a three-manifold be nonreduced?
mathoverflow.net

15
Lie groups vs. algebraic groups and deformations
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15
orbit space of a topological manifold
mathoverflow.net

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