7 papers · 1 filter
Embedded spheres in S^2\times S^1#...#S^2\times S^1
Siddhartha Gadgil
We give an algorithm to decide which elements of pi_2(S^2\times S^1#...#S^2\times S^1) can be represented by embedded spheres. Such spheres correspond to splittings of the free gro…
Heegaard Floer theory and property P
Siddhartha Gadgil
This paper has been withdrawn due to an error in the proof. The paper implicitly assumed that every homotopically trivial knot is related to the unknot by negative crossings, which…
The derived series and virtual Betti numbers
Siddhartha Gadgil
The virtual Betti number conjecture states that any hyperbolic three-manifold has a finite cover with positive first Betti number. We show that this would follow if it were known t…
Contact Structures on elliptic 3-manifolds
Siddhartha Gadgil
We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on preserves a standard…
A proof of a homeomorphism theorem of Waldhausen
Siddhartha Gadgil, Gadde A. Swarup
We give a short proof of Waldhausen's homeomorphism theorem for orientable Haken 3-manifolds.
Equivariant framings, lens spaces and Contact structures
Siddhartha Gadgil
We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable…