A note on the Mond conjecture and crosscap concatenations

Journal of Singularities
volume 12 (2015), 19-26

Received 4 December 2013. Received in revised form 16 September 2014.

DOI: 10.5427/jsing.2015.12b

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Abstract:

We prove the Mond conjecture relating the codimension of a map germ from C^n to C^{n+1} with its image Milnor number for bigerms resulting from the operation of simultaneous augmentation and monic concatenation. We then define a new operation, the crosscap concatenation, in order to obtain new examples of multigerms where the Mond conjecture can be tested.

Keywords:

Mond conjecture, augmentation and concatenation, multigerms

Mathematical Subject Classification:

58K40 (primary), 32S30, 32S70 (secondary)

Author(s) information: