An exasperating exercise from Goursat’s Cours d’Analyse, and other related material, 1962-66.

 

Non-differentiable functions à la F. Riesz and B. Sz.-Nagy, “Functional Analysis”, 1967.

 

A magical definition, from S. Lefschetz, “Introduction to Topology”, 1968.

 

Solution of a problem posed by Professor N. E. Steenrod, 1969.

 

Solution of E 2246, proposed by Andrew Rochman, American Mathematical Monthly, vol.  78 (1971),  p. 676.

 

The de Rham cohomology of  foliated manifolds, Ph. D. Thesis, SUNY Stony Brook (1974), vii + 113 pp.

 

The homological algebra of topological vector spaces, 1975.

 

The canonical chain homotopy of Weil maps, 12 pp.

 

Duality theorems for foliated manifolds,

 

Geometrical microphysics, I and II, 11 + 30 pp.

 

Gravitation and the Schrodinger equation, 10 pp.

 

A six colour theorem for 3-manifolds, 9 pp.

 

A finiteness theorem for foliated manifolds, Journal of the Mathematical Society of Japan, vol. 30 (1978), pp. 687-696.

 

On coloring manifolds, Illinois Journal of Mathematics, vol. 25 (1981), pp. 464-469.

 

A trace formula for compact manifolds, Transactions of the American Mathematical Society, vol. 274 (1982), pp. 85-88.

 

Differential Geometry, Notes 1982? 13 pp.

 

On neighbourly triangulations, Transactions of the American Mathematical Society, vol. 277 (1983), pp. 213-239.

 

Addendum to my paper “On coloring manifolds”,  Illinois Journal of Mathematics, vol. 27 (1983), pp. 612-613.

 

Non-degenerescence of some spectral sequences, Annales de l’institut Fourier, vol. 34 (1984), pp. 39-46.

 

A “Riemann Hypothesis” for triangulable manifolds, Proceedings of the American Mathematical Society, vol. 90 (1984), pp. 325-326.

 

Formal theories are acyclic, Zeitschrift für mathematisches Logik und Grundlagen der Mathematik, vol. 31 (1985), 363-368.

 

Positively curved bilinear forms (joint with S. M. Zoltek), Proceedings of the American Mathematical Society, vol. 97 (1986), pp. 577-584.

 

Embedding and unknotting of some polyhedra, Proceedings of the American Mathematical Society, vol. 100 (1987), pp. 201-203.

 

Heawood inequalities, Journal of Combinatorial Theory A, vol. 46 (1987), pp. 50-78.

 

Unknotting and colouring of polyhedra, Bulletin of the Polish Academy of Sciences, Mathematics, vol. 36 (1988), pp. 661-664.

 

Kneser colorings of polyhedra, Illinois Journal of Mathematics, vol. 33 (1989), pp. 592-620.

 

A generalized Kneser conjecture, Journal of Combinatorial Theory B, vol. 49 (1990), pp. 236-240.

 

Tucker-Ky Fan colorings, Proceedings of the American Mathematical Society, vol. 110 (1990), pp. 1075-1081.

 

A generalized Van Kampen-Flores theorem, Proceedings of the American Mathematical Society, vol. 111 (1991), pp. 559-565.

 

Kuratowski complexes, Topology, vol. 30 (1991), pp. 67-76.

 

Kneser colorings, Van Kampen-Flores theorem, etc., talk, 6 pp.

 

Simplicial 2-complexes which embed, but not linearly, in ú3, 5 pp.

 

Van Kampen Obstructions, 1992, 100 pp.

 

Some combinatorial and topological applications of deleted joins, talk I.H.E.S., 1991, 9 pp.

 

Shifting and embeddability of simplicial complexes, Max-Planck-Institut für Mathematik, Bonn, MPI/92-51, 11 pp. (1992).

 

Linear vs. piecewise-linear embeddability of simplicial complexes (joint with U. Brehm), Max-Planck-Institut für Mathematik, Bonn, MPI/92-52, 12 pp. (1992).

 

A generalized Wu lemma,

 

A one-dimensional Whitney trick and Kuratowski’s graph planarity criterion, Israel Journal of Mathematics, vol. 73 (1991), pp.79-89.

 

Tverberg’s theorem via number fields, Israel Journal of Mathematics, vol. 79 (1992), pp. 317-320.

 

One hundred and thirteen “Reviews” of interesting results, etc.

 

Exterior shifting, Research Bulletin of the Panjab University, Science, vol. 43 (1993),  pp. 259-268.

 

Poincaré’s Papers on Topology, Chandigarh Topology Seminar, Panjab University 1993-1994, iv + 237 pp.

 

Index theorem for foliations, two talks in Instructional Workshop on Cyclic (Co)homology, Panjab University, 1995.

 

From calculus to cyclic cohomology, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, IHES/M/95/82, 8 pp. (1995).

 

Some simplicial (co)homologies, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, IHES/M/95/83, 25 pp. (1995).

 

A look back at Poincaré’s Analysis Situs, in, “Henri Poincaré : Science et Philosophie (Nancy 1994, editors J.-L Greffe, G. Heinzmann and K. Lorenz)”, Akademie Verlag Berlin (1996), pp. 251-258.

 

Ein-stein’s quotient, 1 p.

 

Combinatorial methods in topology, Chandigarh Topology Seminar, Panjab University 1994-1995, vii + 157 pp. (*)

 

Discrete continuous, Oberwolfach 1995.

 

An “odd” Schwarz inequality,  Research Bulletin of the Panjab University, Science, vol. 47 (1997), pp. 215-217.

 

Sierksma’s dutch cheese problem, Mathematical Sciences Research Institute, Berkeley, MSRI 1997-025, 16 pp. (1997).

 

An index formula for Tverberg partitions?, MSRI talk (1997), 8 pp.

 

The zeta function of a simplicial complex (joint with A. Björner), Israel Journal of Mathematics, vol. 103 (1998), pp. 29-40.

 

The topological work of Henri Poincaré, Chapter 6 of  “History of Topology” (ed. I. M. James), Elsevier North-Holland Amsterdam (1999), pp. 123-167.

 

Review of “Stories about Maxima and Minima” by V. M. Tikhomirov, Resonance, vol. 4 (1999), pp. 99-100.

 

Letter to Dushyant, 1 p.

 

On dimensional analysis : “The Bridgman-Buckingham Theorems,” 1999, 5 pp.

 

A minimal triangulation of the Hopf map and its application (joint with K. V. Madahar), Geometriae Dedicata, vol. 105 (2000), pp. 105-114.

 

Tverberg partitions and Borsuk-Ulam theorems, Pacific Journal of Mathematics, vol. 196 (2000), pp. 231-241.

 

On some questions concerning a functional equation involving Möbius transformations, Aequationes Mathematicae, vol. 60 (2000), pp. 137-141.

 

Minimal simplicial self-maps of the 2-sphere (joint with K. V. Madahar), Geometriae Dedicata, vol. 84 (2001), pp. 25-33.

 

The four colour problem, as viewed by Spencer-Brown and Louis Kauffmann. 

 

Taylor’s formula via determinants, College Mathematics Journal, vol. 32 (2001), p. 54.

 

Bénard polygons, Studies in Applied Mathematics, vol. 106 (2001), pp. 139-155.

 

A topological paradox of motion, The Mathematical Intelligencer, vol. 23 (2001), pp. 67-68.

 

F. Chorlton, “A Text Book of Fluid Dynamics” : a critique, etc.

 

A “nice” map colour theorem, Illinois Journal of Mathematics, vol. 46 (2002),  pp. 1111-1123.

 

Stationary states, Acta Universitatis Carolinae,  Mathematica et Physica, vol. 43 (2002), pp. 57-63.

 

Hint ?  Fields Medal !

 

Bryan Sykes, “The Seven Daughters of Eve” : a summary, etc. (2002?) 22pp.

 

How woodborers bore = Tetrahedron ABCD of width 1 with minimum AB+BC+CD, American Mathematical Monthly, vol. 110 (2003), pp. 785-799.

 

On primitive subdivisions of an elementary tetrahedron, Pacific Journal of Mathematics, vol. 211 (2003),  pp. 123-155.

 

Algebraical irreducibilty geometrically, 30 pp.

 

A letter to Professor P. K. Jain (2005), 1 p.

 

Amartya Sen, “The Argumentative Indian” : some impressions (2005), 3 pp.

 

When is the locally nilpotent part a direct summand? (2006), 15 pp.

 

On linear maps, talk BYU (2006), 18 pp.

 

The Forgotten Shaheeds of Dagshai, with a prefatory note, 2007, 50 pp. + 1 p.

 

The Forgotten Shaheeds … (contd.), 2007-8,  32 pp.

 

Jethmalani, 2007, 2 pp.

 

Roots of functions, 2007, 20 pp.

 

Roots of translations, Aequationes Mathematicae, vol. 75 (2008), pp. 304-307.

 

Cacti and mathematics, 2007, 8 pp.

 

Banasar Garhi = Jagatgarh Fort ?

 

On equivelar maps, 2008, 12 pp. (*)

 

Fly, getting sad on a fair amount of alcohol? (10), 2008, 9 pp.

 

Extracts from my notebooks, 2008, 28 pp.

 

Extracts …  (II), 2009, 30 pp. (*)

 

My solutions to IMO 2009 (Bremen) problems, 2009, 5 pp.

 

“213, 16A” and mathematics, 2010, 37 pp.

 

Pseudoku, 2010, 2 pp.

 

How I learnt some well-known folklore, 2010, 3 pp.

 

Plagiarism?, 2011, 2 pp.

 

By far the most important book, 2011, 1 p.

 

Hyperbolic manifolds, 2012, 28 pp.(*)

 

Tweets, 2012, 1 p.

 

From Bina’s garden to Khovanov’s homology, 2012, 8 pp.(*)

 

The joys of forgetting, 2012, 4 pp.

 

Tweaking, 2013, 4 pp.

 

Startling logic, 2013, 4 pp.

 

Straight to Mecca, 2013, 4 pp. (contd.,1 p.)

 

Oxymorons no more!, 2013, 4 pp.

 

Plain geometry & relativity, 2013, 4 pp.

 

Nota bene, in progress (no. 42,  24 solutions, Sankalak)

 

Adieu 2013!, 2013, 1 p.

 

Mirror relativity continued, 2014, 9 pp.

 

A glossary of some Punjabi words, 2014, 29 pp.

 

 

 

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