000136399 001__ 136399
000136399 005__ 20250113143110.0
000136399 0247_ $$2doi$$a10.1016/j.indag.2022.02.007
000136399 0248_ $$2sideral$$a128655
000136399 037__ $$aART-2022-128655
000136399 041__ $$aeng
000136399 100__ $$aAlanís-López, L.
000136399 245__ $$aOn a quadratic form associated with a surface automorphism and its applications to Singularity Theory
000136399 260__ $$c2022
000136399 5060_ $$aAccess copy available to the general public$$fUnrestricted
000136399 5203_ $$aWe 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)
000136399 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033
000136399 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000136399 590__ $$a0.6$$b2022
000136399 591__ $$aMATHEMATICS$$b243 / 329 = 0.739$$c2022$$dQ3$$eT3
000136399 592__ $$a0.445$$b2022
000136399 593__ $$aMathematics (miscellaneous)$$c2022$$dQ2
000136399 594__ $$a1.3$$b2022
000136399 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion
000136399 700__ $$0(orcid)0000-0002-8276-5116$$aArtal, E.$$uUniversidad de Zaragoza
000136399 700__ $$aBonatti, C.
000136399 700__ $$aGómez-Mont, X.
000136399 700__ $$aGonzález Villa, M.
000136399 700__ $$aPortilla Cuadrado, P.
000136399 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología
000136399 773__ $$g33, 4 (2022), 816-843$$pIndag. math.$$tINDAGATIONES MATHEMATICAE-NEW SERIES$$x0019-3577
000136399 8564_ $$s593915$$uhttps://zaguan.unizar.es/record/136399/files/texto_completo.pdf$$yPreprint
000136399 8564_ $$s1805669$$uhttps://zaguan.unizar.es/record/136399/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint
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000136399 951__ $$a2025-01-13-14:30:24
000136399 980__ $$aARTICLE