Fixed point indices and manifolds with collars

1687-1812-2006-87657 1687-1812 Research Article Fixed point indices and manifolds with collars BenjaminChen-Farngchenflben@gmail.com GottliebDaniel Henrygottlieb@math.ucla.edu

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Fixed Point Theory and Applications 1687-1812 2006 2006 1 87657 http://www.fixedpointtheoryandapplications.com/content/2006/1/87657 10.1155/FPTA/2006/87657 712200425420052472005352006 2006Benjamin and GottliebThis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper concerns a formula which relates the Lefschetz number for a map to the fixed point index summed with the fixed point index of a derived map on part of the boundary of . Here is a compact manifold and is with a collar attached.

Nielsen Theory and Related Topics

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Vector fields and transfersBeckerJCGottliebDHManuscripta Mathematica1991722111130BenjaminC-FFixed point indices, transfers and path fields, M.S. thesisPurdue University, Indiana1990Path fields on manifoldsBrownRFTransactions of the American Mathematical Society1965118180191BrownRFThe {L}efschetz Fixed Point TheoremScott, Foresman, Illinois1971vi+186Fixed point index and fixed point theorem for {E}uclidean neighborhood retractsDoldATopology. An International Journal of Mathematics196541810.1016/0040-9383(65)90044-3DoldALectures on Algebraic Topology, Die Grundlehren der mathematischen WissenschaftenSpringer, New York1972200xi+377The fixed point transfer of fibre-preserving mapsDoldAMathematische Zeitschrift1976148321524410.1007/BF01214520Generalized normal bundles for locally-flat imbeddingsFadellETransactions of the American Mathematical Society196511448851310.1090/S0002-9947-1965-0179795-4A de {M}oivre like formula for fixed point theoryGottliebDHFixed Point Theory and Its Applications (Berkeley, CA, 1986), Contemp. Math.American Mathematical Society, Rhode IslandBrown RF19887299105A de Moivre formula for fixed point theoryGottliebDHATAS de 5∘ Encontro Brasiliero de Topologia1988535967Universidade de Sao Paulo, Sao Carlos S.~P., Brasil20919483On the index of pullback vector fieldsGottliebDHDifferential Topology (Siegen, 1987), Lecture Notes in Math.Springer, BerlinKoschorke U19881350167170Zeroes of pullback vector fields and fixed point theory for bodiesGottliebDHAlgebraic Topology (Evanston, IL, 1988), Contemp. Math.American Mathematical Society, Rhode Island198996163180Abbildungsklassen <inline-formula><graphic file="1687-1812-2006-87657-i9.gif"/></inline-formula>-dimensionaler {M}annigfaltigkeitenHopfHMathematische Annalen192796120922410.1007/BF01209163Fibrings of enveloping spacesHuSTProceedings of the London Mathematical Society. Third Series19611169170710.1112/plms/s3-11.1.691Singular points of vector fields under general boundary conditionsMorseMAmerican Journal of Mathematics192951216517810.2307/2370703A path space and the {S}tiefel-{W}hitney classesNashJProceedings of the National Academy of Sciences of the United States of America19554132032110.1073/pnas.41.5.32052808716589673A generalized {P}oincaré index formulaPughCCTopology. An International Journal of Mathematics1968721722610.1016/0040-9383(68)90002-5