Infinite genus surfaces and irrational polygonal billiards

We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus topological real surface with exactly one end.Comment: 15 pages, 18 figure

My Involvement through Community Engagement & Service

Maricar Valdez discusses student engagement at Linfield College with regard to her involvement with First CLAS and Alternative Spring Break.https://digitalcommons.linfield.edu/inauguration2019_students/1016/thumbnail.jp

[Review of] Susan Lobo and Steve Talbot, eds. Native American Voices: A Reader

This valuable collection of readings edited by leading scholars in the field enriches the social science and educational literature for several reasons. First, the book provides a wealth of information for both undergraduate and graduate students. The readings are multidisciplinary, and contain scholarly articles, journalistic selections, documents, oral history and testimony, songs and poetry, maps and charts. The readings encompass a global approach with their foci on Indian peoples of the United States, as well as a few selections of indigenous groups in Canada and Latin America. The book is arranged into nine interrelated parts with discussion questions, key terms, and suggested readings at the end of each part. In short, the articles succeed in bringing to students important materials representing the rich diversity of Native Peoples

The Queerness in Phenomenology: Life As It Is

The question of what “is” someone who is queer in a metaphysical standpoint have been hotly debated in contemporary metaphysics of gender. In my paper I will explore the view of a Phenomenological source and understanding of queerness within the umbrella of gender. Within the realm of gender we can see how queerness is a blob to which gender is both part of and a stand in for the person gender. Using Phenomenological methods based on Husserl’s foundation I can establishes a base for which queerness can be clearly seen. In my paper I will address not only the difference of cis heteronormative phenomenology and the reality that queer people live. This causes a negation in a metaphysical way. The object in which the queer person lives becomes In a way how Hegel understood that if we see a gendered person in the cis reality we can say “this is a man or women” due to the way we correspond cis normative gender. This is where I will try to use Husserl’s “principle of contradiction” and Hegel’s idea of “negation” to show the fluidity of gender in which queerness encompasses. I can clearly demonstrate the “Horizon” in which the limits of cis hetero perspective of understanding of gender and queerness. But in the same thought I will further drive this idea that in a sense the split with in an ontological reality between the lives of cis hetero people and queer people. By giving definitions of what if different such a orientation and performance with the reality that queer people live with such a gender binary ontology. I will then derive some meta-language and construct a realty how communities build themselves from a mutual understanding of this queer ontology. Also real world examples of how the logic of gender effects the way that queer people operate. The counter argument I would argue against a gender nihilism that would try to attack the question that I raise that queerness is a separate state within consciousness. To which I would defended against an individual level of gender identity and understanding. To treat gender in an alienated value. But by using a strong phenomenological structure I would be able to defended by idea that queerness with in gender is a whole different ontological reality that the cis hetero reality. I will then derive some meta-language and construct a realty how communities build themselves from a mutual understanding of this queer ontology.

On the geometry of graphs associated to infinite-type surfaces

Consider a connected orientable surface $S$ of infinite topological type, i.e. with infinitely-generated fundamental group. We describe the large-scale geometry of arbitrary connected subgraphs of the arc complex $A(S)$ and curve complex $C(S)$ of $S$, provided they are invariant under a sufficiently big subgroup of the mapping class group $Mod(S)$. We obtain a number of consequences; in particular we recover the main results of J. Bavard and Aramayona-Fossas-Parlier .Comment: v2: Substantial rewrite, fixes some errors in the previous version. Proposition 1.3 of v1 has now been merged into Theorem 1.1. Theorems 1.6 and 1.11 of v1 were not correct as stated, this has been fixed in v2. Any mention to subgraphs of the curve graph for surfaces with isolated ends was removed, as this case is covered in recent work of Durham-Fanoni-Vlami

Toroidal and Klein bottle boundary slopes

Let M be a compact, connected, orientable, irreducible 3-manifold and T' an incompressible torus boundary component of M such that the pair (M,T') is not cabled. By a result of C. Gordon, if S and T are incompressible punctured tori in M with boundary on T' and boundary slopes at distance d, then d is at most 8, and the cases where d=6,7,8 are very few and classified. We give a simplified proof of this result (or rather, of its reduction process), based on an improved estimate for the maximum possible number of mutually parallel negative edges in the graphs of intersection of S and T. We also extend Gordon's result by allowing either S or T to be an essential Klein bottle. to the case where S or T is a punctured essential Klein bottle.Comment: Preliminary version, updated. We use a new approach that yields a stronger conclusion. 28 pages, 18 figure