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 (1978), 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.
Shifting and embeddability,1988,
21 pp. (*)
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.
SDCP, 1989. 14 pp. (*)
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-
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.
Linear embeddability, 1991, 32 pp. (*)
mli Chapter V. Heawood Inequalities, 1991-2, 67 pp. (*)
Shifting
and embeddability of simplicial complexes, Max-Planck-Institut für
Mathematik,
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, 1992, 5 pp.
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.
Contents of “Reviews” and part I, ii + pp. 1-41; part II, pp. 42-78; part III, pp. 79-120; part IV, pp. 121-158; part V, pp. 159-165 ...
Exterior shifting,
Research Bulletin of the
Reviewer’s Note : on an elegant paper of Schild, 1993, 2 pp.
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,
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
Ein-stein’s quotient, 1 p. (1995).
Combinatorial methods in topology, Chandigarh Topology Seminar, Panjab University 1994-1995, vii + 157 pp. (*)
Discrete ↔ Continuous, Oberwolfach 1995, 5 pp. (*)
An
“odd” Schwarz inequality,
Research Bulletin of the
Sierksma’s
dutch cheese problem, Mathematical Sciences Research Institute,
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, 6 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?) 22 pp.
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.
Adieu IHES (2005), 1 p.
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, 29 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, 33 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 (P G & R), 2013, 4 pp. (*)
Nota bene, 2013-4, 2 pp. (no. 42, 24 solutions, Sankalak)
Adieu 2013!, 2013, 1 p.
Mirror relativity continued (P G & R, part II), 2014, 9 pp. (*)
A glossary of some Punjabi words, 2014, 33 pp. (Punjabi software)
The Forgotten Koh-i-noors of Ranjit Singh, 2014, 6 pp.
More mirror relativity (P G & R, part III), 2014, 7 pp. (*)
More mirror relativity continued (P G & R, part IV), 2015, 6 pp. (*)
Sohn Lal s/o Vaso Mall, 2015, 10 pp.
11833, 2015, 1 p.
auNgLIAW Aqy tweIlW, 2015, 4 pp. (= Fingers and tiles) (e - Q)
Hundred Years Ago, 2015, 1 p.
Switches and
fingers, 2016, 10 pp. (a – A, d-b[1-10)
Who is the best mathematician in the world ?, 2016, 1 p.
Aliens and invisibility (P G & R, part V), 2016, 12 pp. Or PG&R I-V, 2013-2016, 38pp.
bIj gixq dw mUl mslw, 2017, 2
pp. (= The
fundamental problem of algebra)
The fundamental
theorem of algebra, 2017, 5 pp. (e - Q, b[11-28)
aft FTA, 2017, 6 pp. (d-b[1-10)
Emwr iKAwm dI s`B qoN ipAwrI r`cxw, 2017, 2 pp. (= The prettiest composition of Khayyam)
sB qoN ipAwrI
r`cxw, Bwg dUjw, 2018, 5 pp. (= The prettiest
composition, part two)
sB qoN ipAwrI r`cxw, Bwg qIjw, 2018, 12 pp. (= The prettiest composition, part three)
sB qoN ipAwrI r`cxw, Bwg swFy iqMn = pMjwh not, 2018-20,
7 pp. (= The prettiest composition,
part three and a half = Fifty notes)
sB qoN ipAwrI r`cxw, Bwg cOQw, 2019, 10 pp. (= The prettiest composition, part four)
sB qoN ipAwrI
r`cxw, Bwg pMjvW, 2020, 16 pp. (= The prettiest
composition, part five)
Voice recognition, 2020, 3 pp.
in`k-su`k : hobson’s choice, garlands, etc., 2020 →, pp. 1-16.
bing, broom and bamboo man, 2020, 5 pp.
in`k-su`k
: spin, theta, etc., 2021, pp. 17-24
hyvuf dI nwbrwbrI, 2021, 1
p. = The Inequality of Heawood
in`k-su`k : Riemann, Jordan, Pontryagin, S&E (1988), etc., 2021-22, pp. 25-65
Time slows down ..., 2022, 1 p.
Shadows and reflections ..., 2022, 1 page + 2 audios, 3:33 and 3:09 mts
sUrj pirQ`vI dy igrd Gumdw hY, 2022, 1 p. = The sun revolves around the earth
Pontryagin Complexes, 2022, 4 pp. = the “blurb” mentioned on page 59 of my miscellany.
A Turtle’s Tale , 2022, 5 pp.
A pretty theorem in Shahmukhi → اِک پِآری تھیاورم شاہ مُکھی وِچ , 2023, 2 pp. → 6 pp.
Sirsa nadi, 2023, 7 pp.
Map-reading geometry and homeomorphisms, 2023, 7 pp. (*)
Distances and homeomorphisms, 2024, 5 pp.
irKilk dI kONtInuAs &MkSn, hYNsl dy nMbrW ivc,
ijhdw ikqy vI nhIN fYrIvyitv, 2024, 1 p.
kovwlIauskI
dy iek KUbsUrq pypr dw qrjmw, 2024, 3 pp.
Über
Kowalewskis Über Bolzanos nichtdifferenzierbare stetige Funktion,
2024, 1 p.
... but nowhere
differentiable!, 2024, 12 pp.
