Indian Institute of Science

Bangalore 560012, India

*e-mail:
gadgil@math.iisc.ernet.in*

My research is primarily in low-dimensional topology and geometric group theory (though I have made other ventures recently).

- Summary of my research (as of November 2005) and a brief summary of my work done in India (i.e., since July 2002) - Audio version.
- My CV

- Open manifolds, Ozsvath-Szabo invariants and Exotic $\R^4$'s, to appear in Expositiones mathematicae.
- Surfaces of bounded mean curvature in Riemannian manifolds , to appear in Transactions of A.M.S.
- Algebraic and Geometric Intersection numbers for free groups (joint with Suhas Pandit), to appear in Topology and its Applications.
- Real theta characteristics and automorphisms of a real curve (joint with Indranil Biswas), Journal Australian Math. Soc.
- Watson-Crick pairing, the Heisenberg group and Milnor invariants, Journal of Mathematical Biology
- Manifolds with positive isotropic curvature, to appear in the Proceedings of the A.M.S.
- Least-area surfaces and Incompressibility, Expos. Math. 26 (2008), no. 1, 93-98.
- Non-orientable Thom-Pontrjagin constructions and Seifert surfaces (joint with Dishant Pancholi), J. Ramanujan Math. Soc. 23 (2008), no. 2, 143-149.
- On theta characteristics of a compact Riemann surface (joint with I. Biswas and P. Sankaran), Bull. Sci. Math. 131 (2007), no. 5, 493--499.
- Degree-one maps, Surgery and four-manifolds, Bull. Lond. Math. Soc. 39 (2007), no. 3, 419-424.
- Embedded spheres in S^2\times S^1#...#S^2\times S^1, Topology Appl. 153 (2006), no. 7, 1141--1151.
- The Chord algebra and fundamental groups (joint with Lenny Ng), appendix to Knot and braid invariants from contact homology II by Lenny Ng, Geom. Topol. 4 (2005), 1603-1637.
- On the geometric simple connectivity of open manifolds. (joint with Louis Funar) Int. Math. Res. Not. (2004), no. 24, 1193--1248.
- Contact structures on elliptic 3-manifolds. Proc. Amer. Math. Soc. 132 (2004), no. 12, 3705--3714
- Limits of functions and elliptic operators, Proc. Indian Acad. Sci. Math. Sci. 114 (2004), no. 2, 153--158.
- Homology and homeomorphisms of non-orientable surfaces (joint with Dishant Pancholi), Proc. Indian Acad. Sci. Math. Sci. 115 (2005), no. 3, 251--257.
- Extremes of the Indian summer monsoon , (joint with Sulochana Gadgil, P.N. Vinaychandran and P.A. Francis) Geophysical Research letters 2004.
- Equivariant framings, lens spaces and contact structures. Pacific J. Math. 208 (2003), no. 1, 73--84.
- Cobordisms and Reidemeister torsions of homotopy lens spaces, Geom. Topol. 5 (2001), 109-125.
- The $pq$-condition for $3$-manifold groups , Proc. Amer. Math. Soc. 129 (2001), no. 6, 1873-1875.
- Topological geodesics and virtual rigidity (joint with Louis Funar), Algebr. Geom. Topol. 1 (2001), 369-380.

Preprints

- A triangulation of a homotopy Deligne-Mumford compactification of Moduli space, submitted for publication.
- A chain
complex and quadrilaterals for normal surfaces (joint with
Tejas Kalelkar), submitted for publication.

- One-handles and Concordance kernels of smooth 4-manifolds, submitted for publication..
- Degree-one maps and Akbulut corks, preprint.
- On the Andrews-Curtis conjecture and algorithms from topology, preprint
- The derived series and virtual Betti numbers., preprint
- Conformal structures and harmonic functions (joint with Harish Seshadri), preprint

- Ricci flow and the Poincare conjecture : joint with Harish Seshadri.
- Dynamics on the circle : article in Resonance.
- Symmetries of spheres : PDF slides for a lecture to the Indian Academy of Sciences (not designed to be self-contained).
- Chern and total curvature , article in Resonance.

- A topological characterisation of hyperbolic spaces (following Bowditch).
- Knotted Tori.
- Lectures notes on 3-manifold topology: Connected sums and prime decompositions, Heegaard splittings and Dehn surgery .
- Lecture notes on delta-hyperbolic spaces