136399 20260212204405.0 doi 10.1016/j.indag.2022.02.007 sideral 128655 ART-2022-128655 eng Alanís-López, L. On a quadratic form associated with a surface automorphism and its applications to Singularity Theory 2022 Access copy available to the general public Unrestricted We study the nilpotent part N' of a pseudo-periodic automorphism h of a real oriented surface with boundary S. We associate a quadratic form Q defined on the first homology group (relative to the boundary) of the surface S. Using the twist formula and techniques from mapping class group theory, we prove that the form Q~ obtained after killing kerN is positive definite if all the screw numbers associated with certain orbits of annuli are positive. We also prove that the restriction of Q~ to the absolute homology group of S is even whenever the quotient of the Nielsen–Thurston graph under the action of the automorphism is a tree. The case of monodromy automorphisms of Milnor fibers S=F of germs of curves on normal surface singularities is discussed in detail, and the aforementioned results are specialized to such situation. This form Q is determined by the Seifert form but can be much more easily computed. Moreover, the form Q~ is computable in terms of the dual resolution or semistable reduction graph, as illustrated with several examples. Numerical invariants associated with Q~ are able to distinguish plane curve singularities with different topological types but same spectral pairs. Finally, we discuss a generic linear germ defined on a superisolated surface. In this case the plumbing graph is not a tree and the restriction of Q~ to the absolute monodromy of S=F is not even. © 2022 Royal Dutch Mathematical Society (KWG) info:eu-repo/grantAgreement/ES/DGA/E22-20R info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033 info:eu-repo/semantics/openAccess by-nc-nd https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 0.6 2022 MATHEMATICS 243 / 329 = 0.739 2022 Q3 T3 0.445 2022 Mathematics (miscellaneous) 2022 Q2 1.3 2022 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Artal, E. Universidad de Zaragoza (orcid)0000-0002-8276-5116 Bonatti, C. Gómez-Mont, X. González Villa, M. (orcid)0000-0002-0370-3401 Portilla Cuadrado, P. 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 33, 4 (2022), 816-843 Indag. math. INDAGATIONES MATHEMATICAE-NEW SERIES 0019-3577 503968 http://zaguan.unizar.es/record/136399/files/texto_completo.pdf Postprint 1794232 http://zaguan.unizar.es/record/136399/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:136399 articulos driver 2026-02-12-20:41:28 ARTICLE