%0 Generic %1 kourliouros2018milnorpalamodov %A Kourliouros, Konstantinos %D 2018 %K Milnor Paramodov theorem %T The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities %U http://arxiv.org/abs/1811.07422 %X In this note we give a simple proof of the following relative analog of the well known Milnor-Palamodov theorem: the Bruce-Roberts number of a function relative to an isolated hypersurface singularity is equal to its topological Milnor number (the rank of a certain relative (co)homology group) if and only if the hypersurface singularity is quasihomogeneous. The proof relies on an interpretation of the Bruce-Roberts number in terms of differential forms and the Lê-Greuel formula.

@misc{kourliouros2018milnorpalamodov, abstract = {In this note we give a simple proof of the following relative analog of the well known Milnor-Palamodov theorem: the Bruce-Roberts number of a function relative to an isolated hypersurface singularity is equal to its topological Milnor number (the rank of a certain relative (co)homology group) if and only if the hypersurface singularity is quasihomogeneous. The proof relies on an interpretation of the Bruce-Roberts number in terms of differential forms and the L\^e-Greuel formula.}, added-at = {2018-11-20T15:27:57.000+0100}, author = {Kourliouros, Konstantinos}, biburl = {https://www.bibsonomy.org/bibtex/228e2551634475cd96cedfbc209898e44/taka3617}, description = {The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities}, interhash = {a3f9ac62737040ae607e3d430a3cf9b2}, intrahash = {28e2551634475cd96cedfbc209898e44}, keywords = {Milnor Paramodov theorem}, note = {cite arxiv:1811.07422}, timestamp = {2018-11-20T15:27:57.000+0100}, title = {The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities}, url = {http://arxiv.org/abs/1811.07422}, year = 2018 }