Note: In my research community, we tend to list authors of joint publications in alphabetical order, unless dictated by submission circumstances. All authors are expected to have equally substantial intellectual contribution to the paper. In particular, we kindly request not to apply the algorithm of This Cartoon to our lists ;-)

Book: T. Kaczynski, K. Mischaikow, et M. Mrozek, Computational Homology , Appl. Math. Sci. Vol. 157, Springer Verlag , NY 2004.

Research papers (Titles in blue are linked to PDF files of either author's preprint versions or open access publications)

M. Allili, T. Kaczynski,  C. Landi, and F. Masoni, Acyclic partial matchings for multidimensional persistence: algorithm and combinatorial Interpretation, published version in J Math Imaging Vis (2018), DOI 10.1007/s10851-018-0843-8.
M. Allili, T. Kaczynski,  C. Landi, and Filippo Masoni, Algorithmic construction of acyclic partial matchings for multidimensional persistence, in Discrete Geometry for Computer Imagery, eds. W.G. Kropatsch, N.M. Artner, I. Janusch, Proc. 20th IAPR Intl. Conf., DGCI 2017 Vienna, Springer 2017, 375-387.
B. Batko, T. Kaczynski, M. Mrozek, and T. Wanner, Linking combinatorial and classical dynamics, preprint arXiv:1710.05802 [math.DS], 16 Oct 2017.
M. Allili, T. Kaczynski,  C. Landi, and Filippo Masoni, A new matching algorithm for multidimensional persistence, preprint ArXiv:1511.05427v3 [cs.CG] 23 March 2017.
T. Kaczynski, M. Mrozek, and T. Wanner, Towards a formal tie between combinatorial and classical vector field dynamics, published version in J. Comput. Dynamics,  3 (1), (2016), 17-50.
C.J. Batkam, F. Colin, and T. Kaczynski,  On differential systems with strongly indefinite variational structure, J. Fixed Point Theory & Appl. , 313-336, DOI 10.1007/s11784-015-0213-8.
M. Allili, T. Kaczynski, and C. Landi,  Reducing complexes in multidimensional persistent homology theory, ArXiv:1310.8089v2 [cs.CG] 12 March 2015, published version in J. Symbolic Computation 78 (2017), 61–75.
M. Ethier and T. Kaczynski, Suspension models for testing shape similarity methods, published version in Special Session on Computational Topology in Image Context, eds. M. Ferri and P. Frosini, Computer Vision & Image Understanding 121 (2014), 13-20.
N. Cavazza, M. Ethier, P. Frosini, T. Kaczynski, and C. Landi, Comparison of persistent homologies for vector functions: from continuous to discrete and back, published version in Computers & Math. 66 (4) (2013), 560-573, DOI 10.1016/j.camwa.2013.06.004.
T. Kaczynski and M. Mrozek, The cubical cohomology ring: an algorithmic approach, Foundations of Comput. Math, 13 (5) (2013), 789–818, DOI 10.1007/s10208-012-9138-4 (open access).
M. Allili, D. Corriveau, S. Derivière, M. Ethier, and T. Kaczynski, Detecting critical regions in multidimensional data sets, published version in Computers & Math. Appl. 61 (2) (2011), 499-512.
P. Dłotko, T. Kaczynski, M. Mrozek, and T. Wanner, Coreduction homology algorithm for regular CW-complexes, Discrete & Comput. Geom. 46 (2) (2011), 361-388 (open access). 
T. Kaczynski (presenter), P. Dłotko, and M. Mrozek, Computing The Cubical Cohomology Ring, in Proc. Computational Topology in Image Context, Chipiona 2010, Image-A 1(1) (2010), 137-142 (open access).
M. Allili, M. Ethier, and T. Kaczynski, Critical region analysis of scalar fields in arbitrary dimensions, published version in Proc. SPIE-IS&T Electronic Imaging, Visualization and Data Analysis, 7530 (2010), 7530–7537.
S. Derivière, T. Kaczynski, and P.O. Vallerand, On the decomposition and local degree of multiple saddles, published version in Annales Sci. Math. Qué. 33 (1) (2009), 45-62.
T. Kaczynski, Multivalued maps as a tool in modeling and rigorous numerics, published version in Browder Festschrift, J. Fixed Point Theory and Appl., 4 (2) (2008), 151-176.
M. Allili, D. Corriveau, S. Derivière, T. Kaczynski, and A. Trahan, Discrete dynamical system framework for construction of connections between critical regions in lattice height data, published version in J. Mathematical  Imaging and Vision, 28 (2) (2007), 99-111.
T. Kaczynski, M. Mrozek, and A. Trahan, Ideas from Zariski topology in the study of cubical sets, cubical maps, and their homology, published version in Canad. J. Math., 59 (5) (2007), 1008-1028.
T. Kaczynski, K. Mischaikow, and M. Mrozek, Computing homology , Homology, Homotopy & Appl., 5 (2) 2003, 233-256.
T. Kaczynski, Recursive coboundary formula for cycles in acyclic chain complexes, Top. Meth. Nonlin. Anal. 18 (2) (2002),351-372.
M. Allili and T. Kaczynski, Geometric construction of a coboundary of a cycle, Discrete & Comput. Geom. 25 (2001), 125-140.
M. Allili and T. Kaczynski, An algorithmic approach to the construction of homomorphismes induced by maps in homology, Trans. Amer. Math. Soc. 352 (2000), 2261-2281, (open access).
T. Kaczynski, Conley index for set-valued maps: From theory to computation, in Conley Index Theory, pp 57-65, Banach Center Publ. Vol 47, Polish Acad. Sci., Warszawa 1999.
T. Kaczynski, M. Mrozek, and M. Slusarek, Homology computation by reduction of chain complexes, published version in Computers & Math. Appl. 35 (4) (1998), 59-70.
M. Allili and T. Kaczynski, Stability of index pairs for flows (summary of [8]), in Proc. Conf. Top. Meth. in Diff. Equ. and Dyn. Sys., Univ. Jagel. Acta Math. 36 (1998).
M. Allili and T. Kaczynski, Stability of index pairs for flows, in Proc. of the 2nd WorldCongress of Nonlinear Analysts (ed. V. Lakshmikantham), Nonlinear Anal. 30 (7) (1997), 4133-4122.
T. Kaczynski and M. Mrozek, Connected simple systems and the Conley functor, Topol. Meth. Nonlin. Anal. 10 (1) (1997) 183-193.
T. Kaczynski and M. Mrozek, Stable index pairs for discrete dynamical systems, Canad. Math. Bull. 40 (4) (1997), 448-455.
M. Frigon, L. Gòrniewicz and T. Kaczynski, Differential inclusions and implicit equations on closed subsets of Rn, in Proc. of the First World Congress of Nonlinear Analysts '92, ed. V. Lakshmikantham, W. de Gruyter, Berlin - New York 1996, 1797-1806.
T. Kaczynski and M. Mrozek, Conley index for discrete multivalued dynamical systems, Topology and Its Appl. 65 (1995) 83-96.
G. Fournier, L. Gòrniewicz and T. Kaczynski, Essential critical points in product manifolds, Rocky Mountain J. Math. 25, 1(1995), 899-907.
T. Kaczynski and R. Srzednicki, Periodic solutions of certain planar rational ordinary differential equations with periodic coefficients, Diff. and Integral Equ.7 (1) 1994, 37-47.
M. Frigon and T. Kaczynski, Boundary value problems for systems of implicit differential equations, J. Math. Anal. and Appl. (1993) 179(2) 1993, 317-326.
T. Kaczynski and H. Xia, Hopf bifurcation for implicit neutral functional differential equations, Canad. Math. Bull. 36 (3) 1993, 286-295.
T. Kaczynski and W. Krawcewicz, A local Hopf bifurcation theorem for a certain class of implicit differential equations, Canad. Math. Bull. 36 (2) 1993, 183-189.
T. Kaczynski and J. Wu, A topological transversality theorem for multi-valued maps in locally convex spaces with applications to neutral equations , Canad. J. Math. 44 (5) 1992, 1003-1013.
T. Kaczynski, Unbounded multivalued Nemytskii operators in Sobolev spaces and their applications to discontinuous nonlinearity , Rocky Mountain J. Math. 22 (2) 1992, 635-643.
T. Kaczynski, Implicit differential equations which are not solvable for the highest derivative, in Delay Differential Equations and Dynamical Systems, Lecture Notes in Math. 1475, Springer, Berlin 1991, 218-224.
L.H. Erbe, W. Krawcewicz, and T. Kaczynski, Solvability of two-point boundary value problems for systems of nonlinear differential equations of the form y''=g(t,y,y',y''), Rocky Mtn. J. Math., 20 (4) (1990), 899-907.
T. Kaczynski and V. Zeidan, An application of Ky-Fan fixed point theorem to an optimization problem, J. Nonlin. Anal. -TMA, 13 (3) 1989, 259-262.
T. Kaczynski, On differential inclusions of second order , in Proc. of the Equadiff 1987 Conf. (eds. C.M. Dafermos, G. Ladas, G. Papanicolau), Lecture Notes in Pure & Appl. Math. Marcel Dekker 1989, 343-352.
T. Kaczynski and W. Krawcewicz, Solvability of boundary value problems for the inclusion  utt - uxx in g(t,x,u) via the A-proper mapping theory , Zeitschrift für Analysis und Ihre Anwendungen, 7 (4) 1988, 337-346.
T. Kaczynski, An extension of the Borsuk fixed point theorem , Bull. Acad. Pol. Sci. 35(5-6) 1987, 315-319.
K. Geba, A. Granas, T. Kaczynski, and W. Krawcewicz, Homotopie et équations non linéaires dans les espaces de Banach, C.R. Acad. Sci. Paris, 300, série I, 1985, 303-306.
T. Kaczynski, Quelques théorèmes de points fixes dans des espaces ayant suffisamment de fonctionnelles linéaires , C.R. Acad. Sci. Paris, 296, série I, 1983, 873-874. 
Papers popularizing mathematics

S. Derivière, A. Trahan, and T. Kaczynski, Comment compter les trous dans une meule de fromage suisse : ou, l'homologie pour les gourmands, in Actes du Congrès AMQ Sherbrooke 2006, (2008), 127-131.
T. Kaczynski, Vivre en dimension 4 and Voyager en dimension 4, Accromath (open access), 1 (2006), 30-35.
T. Kaczynski, Life and travel in 4D, Pi in the Sky (open access), Dec. 2001.
T. Kaczynski, The red violin of science, Pi in the Sky, Dec. 2000.