167 research outputs found
Iron rings, Doctor Honoris Causa Raoul Bott, Carl Herz, and a hidden hand
No full textAn edited and reformatted version of this paper, with an additional photo, will appear in a volume dedicated to Raoul Bott. The author hopes to expand on some aspects of this preprint in future versions.The degree of Doctor of Sciences, honoris causa, was conferred on Raoul Bott by McGill University in 1987. Much of the work to make this happen was done by Carl Herz. Some of the author's personal recollections of both professors are included, along with some context for the awarding of this degree and ample historical tangents. Some cultural aspects occurring in the addresses are elaborated on, primarily, the Canadian engineer's iron ring. This paper also reprints both the convocation address of Raoul Bott and the presentation of Carl Herz on that occasion
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Morse-Bott Embedded Contact Homology
No full textThis dissertation constructs a Morse-Bott version of embedded contact homology (ECH). The dissertation is comprised of two parts, corresponding to the two papers written by the author as a graduate student at UC Berkeley. The first part explains how to compute ECH in the Morse-Bott setting when certain transversality conditions are met and provided a certain correspondence theorem is true; and gives a large class of examples where the transversality conditions are satisfied. The second part provides the analytic foundations of the first part by giving a proof of the correspondence theorem
Localization of Bott-Chern classes and Hermitian residues
No full textWe develop a theory of Cech-Bott-Chern cohomology and in this context we naturally come up with the relative Bott-Chern cohomology. In fact, Bott-Chern cohomology has two relatives and they all arise from a single complex. Thus, we study these three cohomologies in a unified way and obtain a long exact sequence involving the three. We then study the localization problem of characteristic classes in the relative Bott-Chern cohomology. For this, we define the cup product and integration in our framework and we discuss local and global duality morphisms. After reviewing some materials on connections, we give a vanishing theorem relevant to our localization. With these, we prove a residue theorem for vector bundles admitting a Hermitian connection compatible with an action of the non-singular part of a singular distribution. As a typical case, we discuss the action of a distribution on the normal bundle of an invariant submanifold (the so-called Camacho-Sad action) and give a specific example
Endomorphisms of Fano 3-folds and log Bott vanishing
No full textKawakami and the author showed that a projective variety with an
int-amplified endomorphism of degree invertible in the base field satisfies
Bott vanishing. That was a new way to analyze which varieties have nontrivial
endomorphisms. In this paper, we extend that result to a logarithmic version of
Bott vanishing for an endomorphism with a totally invariant divisor.
We apply this to Fano 3-folds. Meng-Zhang-Zhong showed that the only smooth
complex Fano 3-folds that admit an int-amplified endomorphism are the toric
ones. Also, Achinger-Witaszek-Zdanowicz showed that the only smooth complex
Fano 3-folds that are images of toric varieties are the toric ones. Using log
Bott vanishing, we reprove both results and extend them to characteristic p,
for morphisms of degree prime to p.Comment: 17 page
Stability of Bott--Samelson Classes in Algebraic Cobordism
No full textIn this paper, we construct stable Bott--Samelson classes in the projective
limit of the algebraic cobordism rings of full flag varieties, upon an initial
choice of a reduced word in a given dimension. Each stable Bott--Samelson class
is represented by a bounded formal power series modulo symmetric functions in
positive degree. We make some explicit computations for those power series in
the case of infinitesimal cohomology. We also obtain a formula of the
restriction of Bott--Samelson classes to smaller flag varieties.Comment: 23 pages. Comments are welcom
Morse–Bott split symplectic homology
No full text© 2019, The Author(s). We associate a chain complex to a Liouville domain (W¯ , d λ) whose boundary Y admits a Boothby–Wang contact form (i.e. is a prequantization space). The differential counts Floer cylinders with cascades in the completion W of W¯ , in the spirit of Morse–Bott homology (Bourgeois in A Morse–Bott approach to contact homology, Ph.D. Thesis. ProQuest LLC, Stanford University, Ann Arbor 2002; Frauenfelder in Int Math Res Notices 42:2179–2269, 2004; Bourgeois and Oancea in Duke Math J 146(1), 71–174, 2009). The homology of this complex is the symplectic homology of W (Diogo and Lisi in J Topol 12:966–1029, 2019). Let X be obtained from W¯ by collapsing the boundary Y along Reeb orbits, giving a codimension two symplectic submanifold Σ. Under monotonicity assumptions on X and Σ , we show that for generic data, the differential in our chain complex counts elements of moduli spaces of cascades that are transverse. Furthermore, by some index estimates, we show that very few combinatorial types of cascades can appear in the differential
Sign Convention for ∞-Operations in Bott-Morse Case
No full textWe describe the sign and orientation issue appearing in the filtered ∞-formulae in Lagrangian Floer theory using the de Rham model in the Bott-Morse setting. After defining filtered ∞-operations in a Fukaya category, we verify the filtered ∞-formulae.The author is partially supported by JSPS Grant-in-Aid for Scientific Research 19H00636, 24H00182. He is also grateful for the National Center for Theoretical Sciences, Taiwan, where a part of this work was carried out
0336: Henry Bott Journal, 1825-1908
No full textThis collection consists of a unique mixed used scrapbook, journal, and commonplace book. The base book is a published volume about school systems in Pennsylvania in 1881. The author, Henry Bott, pasted in ten multi-page reminiscences on the following topics: “School in York County [PA] in Country Schools ¾ of a Century Ago [Circa 1825]”, “Turnpikes in Olden Times [before railroads]”, “The Old Homestead”, “Seven Valley: Among the Graves of the Departed”, “Progress in Church Work”, “When the Writer Saw the Meteors Fall [1833]”, “A Wanderer”, “A Short History of the Borough of Seven Valley”, “Before the Days of Postage Stamps”, and “Progress”. The vignettes are dated between 1890-1892 and are stated as being recopied in 1908.
The book also features extensive paste-ins of magazine clippings featuring traditional Gibson Girl illustrations as well as illustrations of women with children taken from books and magazines. Also included are two newspaper clippings, including an obituary for Henry Bott and an account of farming by William Albright of Hanover, PA. The back cover of the book features the following names: Mrs. Elmer E. McLevitt(?) and Mrs. Rachel Wilson
A Morse-Bott approach to monopole Floer homology and the triangulation conjecture
No full textIn the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a {\rm spin}^c structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture
Citric acid wastewater as electron donor for biological sulfate reduction
No full textCitrate-containing wastewater is used as electron donor for sulfate reduction in a biological treatment plant for the removal of sulfate. The pathway of citrate conversion coupled to sulfate reduction and the microorganisms involved were investigated. Citrate was not a direct electron donor for the sulfate-reducing bacteria. Instead, citrate was fermented to mainly acetate and formate. These fermentation products served as electron donors for the sulfate-reducing bacteria. Sulfate reduction activities of the reactor biomass with acetate and formate were sufficiently high to explain the sulfate reduction rates that are required for the process. Two citrate-fermenting bacteria were isolated. Strain R210 was closest related to Trichococcus pasteurii (99.5% ribosomal RNA (rRNA) gene sequence similarity). The closest relative of strain S101 was Veillonella montepellierensis with an rRNA gene sequence similarity of 96.7%. Both strains had a complementary substrate range.BiotechnologyApplied Science
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