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Books on the topic 'Finite topological spaces'

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Published: 17 February 2024

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1

Barmak, Jonathan A. Algebraic Topology of Finite Topological Spaces and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22003-6.

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2

Barmak, Jonathan A. Algebraic topology of finite topological spaces and applications. Heidelberg: Springer, 2011.

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3

Engelking, Ryszard. Theory of dimensions, finite and infinite. Lemgo, Germany: Heldermann, 1995.

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4

Talsi, Jussi. Imbeddings of equivariant complexes into representation spaces. Helsinki: Suomalainen Tiedeakatemia, 1994.

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5

Spaces of constant curvature. 6th ed. Providence, R.I: AMS Chelsea Pub., 2011.

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6

Jaco, William H. Topology and geometry in dimension three: Triangulations, invariants, and geometric structures : conference in honor of William Jaco's 70th birthday, June 4-6, 2010, Oklahoma State University, Stillwater, OK. Providence, R.I: American Mathematical Society, 2011.

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7

Stanford Symposium on Algebraic Topology: Applications and New Directions (2012 : Stanford, Calif.), ed. Algebraic topology: Applications and new directions : Stanford Symposium on Algebraic Topology: Applications and New Directions, July 23--27, 2012, Stanford University, Stanford, CA. Providence, Rhode Island: American Mathematical Society, 2014.

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8

1953-, Campillo Antonio, ed. Zeta functions in algebra and geometry: Second International Workshop on Zeta Functions in Algebra and Geometry, May 3-7, 2010, Universitat de Les Illes Balears, Palma de Mallorca, Spain. Providence, R.I: American Mathematical Society, 2012.

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9

1980-, Blazquez-Sanz David, Morales Ruiz, Juan J. (Juan José), 1953-, and Lombardero Jesus Rodriguez 1961-, eds. Symmetries and related topics in differential and difference equations: Jairo Charris Seminar 2009, Escuela de Matematicas, Universidad Sergio Arboleda, Bogotá, Colombia. Providence, R.I: American Mathematical Society, 2011.

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10

Richmond, Thomas Alan. Finite-point order compactifications. 1986.

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11

Barmak, Jonathan A. Algebraic Topology of Finite Topological Spaces and Applications. Springer, 2011.

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12

Tretkoff, Paula. Topological Invariants and Differential Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0002.

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This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number e(X). The Euler number, also known as the Euler-Poincaré characteristic, is an important invariant of a topological space X. It generalizes the notion of the cardinality of a finite set. The chapter presents the simple formulas for computing the Euler-Poincaré characteristic (Euler number) of many of the spaces to be encountered throughout the book. It also discusses fundamental groups and covering spaces and some basics of the theory of complex manifolds and Hermitian metrics, including the concept of real manifold. Finally, it provides some general facts about divisors, line bundles, and the first Chern class on a complex manifold X.

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13

Hrushovski, Ehud, and François Loeser. A closer look at the stable completion. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0005.

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This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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14

Kedlaya, Kiran S., Debargha Banerjee, Ehud de Shalit, and Chitrabhanu Chaudhuri. Perfectoid Spaces. Springer Singapore Pte. Limited, 2022.

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15

Homotopy of Operads and Grothendieck-Teichmuller Groups : Part 1: The Algebraic Theory and Its Topological Background. American Mathematical Society, 2017.

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16

Putnam, Ian F. Cantor Minimal Systems. American Mathematical Society, 2018.

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17

Perfectoid Spaces: Lectures from the 2017 Arizona Winter School. American Mathematical Society, 2019.

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18

Tu, Loring W. Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.001.0001.

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Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah–Bott and Berline–Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, the book begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.

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19

Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-Proper Settings. American Mathematical Society, 2017.

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