My research concerns compact Lie group actions on smooth manifolds and CW complexes. The methods and tools which I use to solve problems go back to algebraic and geometric topology, including topics from the cohomology theory of manifolds (e.g., Smith Theory), the theory of vector bundles and topological K-theory, differential topology (e.g., equivariant thickening and surgery on manifolds) and the theory of groups and their representations.
Selected research papers Krzysztof M. Pawałowski, Group actions with inequivalent representations at fixed points, Math. Zeitschrift, Vol. 187 (1984), 29-47.  Krzysztof M. Pawałowski, Fixed point sets of smooth group actions on disks and Euclidean spaces, Topology, Vol. 28 (1989), 273-289. Corrections: ibid.~35 (1996), 749-750.  Erkki Laitinen, Masaharu Morimoto, Krzysztof M. Pawałowski, Deleting–Inserting Theorem for smooth actions of finite nonsolvable groups on spheres, Commentarii Mathematici Helvetici, Vol. 70 (1995), 10-38.  Krzysztof M. Pawałowski, Chern and Pontrjagin numbers in perfect symmetries of spheres,K-theory, Vol. 13 (1998), 41-55.  Masaharu Morimoto, Krzysztof M. Pawałowski, Equivariant wedge sum construction of finite contractible G-CW complexes with G-vector bundles, Osaka Journal of Mathematics, Vol. 36 (1999), 767-781.  Masaharu Morimoto, Krzysztof M. Pawałowski, The Equivariant Bundle Subtraction Theorem and its applications, Fundamenta Mathematicae, Vol. 161 (1999), 279-303.  Erkki Laitinen, Krzysztof M. Pawałowski, Smith equivalence of representations for finite perfect groups, Proceedings of the American Mathematical Society, Vol. 127 (1999), 297-307.  Krzysztof M. Pawałowski, Manifolds as fixed point sets of smooth compact Lie group actions, Current Trends in Transformation Groups, A. Bak, M. Morimoto, F. Ushitaki (eds), K-Monographs in Mathematics 7, Kluwer Academic Publishers (2002), 79-104.  Krzysztof M. Pawałowski, Ronald Solomon, Smith equivalence and finite Oliver groups with Laitinen number 0 or 1, Algebraic & Geometric Topology, Vol. 2 (2002), 843-895.  Masaharu Morimoto, Krzysztof M. Pawałowski, Smooth actions of finite Oliver groups on spheres, Topology, Vol. 42 (2003), 395-421.  Krzysztof M. Pawałowski, Smooth circle actions on highly symmetric manifolds, Mathematische Annalen, Vol. 341 (2008), 845-858.  Bogusław Hajduk, Krzysztof M. Pawałowski, Aleksy Tralle, Non-symplectic smooth circle actions on symplectic manifolds, Mathematica Slovaca, Vol. 62 (2012), 539-550.  Krzysztof M. Pawałowski, Toshio Sumi, The Laitinen Conjecture for finite non-solvable groups, Proceedings of the Edinburgh Mathematical Society, Vol. 56 (2013), 303–336.  Marek Kaluba, Krzysztof M. Pawałowski, Group actions on complex projective spaces via group actions on disks and spheres, The Topology and the Algebraic Structures of Transformation Groups, RIMS Kôkyûroku, Vol. 1922 (2014), 147-153.  Krzysztof M. Pawałowski, The Smith Equivalence Problem and the Laitinen Conjecture, Handbook of Group Actions, Vol. III, Advanced Lectures in Mathematics, Vol. 40, International Press of Boston (2018), pp. 485-538.  Krzysztof M. Pawałowski, Jan Pulikowski, Smooth actions of p-toral groups on Z-acyclic manifolds, Proceedings of the Steklov Institute of Mathematics, Vol. 305 (2019), pp. 262-269.