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  • 1.
    Benedetti, Bruno
    Free Univ Berlin, Germany.
    Discrete Morse theory for manifolds with boundary2012In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 364, no 12, p. 6631-6670Article in journal (Refereed)
    Abstract [en]

    We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain "Relative Morse Inequalities" relating the homology of the manifold to the number of interior critical cells. We also derive a Ball Theorem, in analogy to Forman's Sphere Theorem. The main corollaries of our work are: (1) For each d ≥ 3 and for each k ≥ 0, there is a PL d-sphere on which any discrete Morse function has more than k critical (d -1)-cells. (This solves a problem by Chari.) (2) For fixed d and k, there are exponentially many combinatorial types of simplicial d-manifolds (counted with respect to the number of facets) that admit discrete Morse functions with at most k critical interior (d -1)-cells. (This connects discrete Morse theory to enumerative combinatorics/ discrete quantum gravity.) (3) The barycentric subdivision of any simplicial constructible d-ball is collapsible. (This "almost" solves a problem by Hachimori.) (4) Every constructible ball collapses onto its boundary minus a facet. (This improves a result by the author and Ziegler.) (5) Any 3-ball with a knotted spanning edge cannot collapse onto its boundary minus a facet. (This strengthens a classical result by Bing and a recent result by the author and Ziegler.)

  • 2.
    Benedetti, Bruno
    et al.
    Freie Universität Berlin, Germany.
    Ziegler, Günter
    On locally constructible spheres and balls2011In: Acta Mathematica, ISSN 0001-5962, E-ISSN 1871-2509, Vol. 206, no 2, p. 205-243Article in journal (Refereed)
    Abstract [en]

    Durhuus and Jonsson (1995) introduced the class of “locally constructible” (LC) 3-spheres and showed that there are only exponentially many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity. We characterize the LC property for d-spheres (“the sphere minus a facet collapses to a (d−2)-complex”) and for d-balls. In particular, we link it to the classical notions of collapsibility, shellability and constructibility, and obtain hierarchies of such properties for simplicial balls and spheres. The main corollaries from this study are: – Not all simplicial 3-spheres are locally constructible. (This solves a problem by Durhuus and Jonsson.) There are only exponentially many shellable simplicial 3-spheres with given number of facets. (This answers a question by Kalai.) – All simplicial constructible 3-balls are collapsible. (This answers a question by Hachimori.) – Not every collapsible 3-ball collapses onto its boundary minus a facet. (This property appears in papers by Chillingworth and Lickorish.)

  • 3.
    Salemi, Arash
    et al.
    KTH, School of Information and Communication Technology (ICT), Integrated Devices and Circuits.
    Buono, Benedetto
    KTH, School of Information and Communication Technology (ICT), Integrated Devices and Circuits.
    Hallén, Anders
    KTH, School of Information and Communication Technology (ICT), Integrated Devices and Circuits.
    Ul Hassan, Jawad
    Bergman, Peder
    Zetterling, Carl Mikael
    KTH, School of Information and Communication Technology (ICT), Integrated Devices and Circuits.
    Östling, Mikael
    KTH, School of Information and Communication Technology (ICT), Integrated Devices and Circuits.
    Fabrication and Design of 10 kV PiN Diodes Using On-axis 4H-SiC2014In: Materials Science Forum, ISSN 0255-5476, E-ISSN 1662-9752, Vol. 778-780, p. 836-840Article in journal (Refereed)
    Abstract [en]

    10 kV PiN diodes using on-axis 4H-SiC were designed, fabricated, and measured. A lifetime enhancement procedure was done by carbon implantation followed by high temperature annealing to increase lifetime to above 2 mu s. The device simulation software Sentaurus TCAD has been used in order to optimize the diode. All fabricated diodes are fully functional and have a V-F of 3.3 V at 100 A/cm(2) at 25 degrees C, which was decreased to 3.0 V at 300 degrees C.

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