The energy of a simplicial complex

[1]  Stefan Friedl Algebraic topology , 2020, Graduate Studies in Mathematics.

[2]  Oliver Knill,et al.  Poincare Hopf for vector fields on graphs , 2019, ArXiv.

[3]  Oliver Knill,et al.  Energized simplicial complexes , 2019, ArXiv.

[4]  Oliver Knill,et al.  A parametrized Poincare-Hopf Theorem and Clique Cardinalities of graphs , 2019, ArXiv.

[5]  Oliver Knill,et al.  More on Numbers and Graphs , 2019, ArXiv.

[6]  Oliver Knill,et al.  Dehn-Sommerville from Gauss-Bonnet , 2019, ArXiv.

[7]  Oliver Knill,et al.  A Reeb sphere theorem in graph theory , 2019, ArXiv.

[8]  S. Mukherjee,et al.  A simple elementary proof of “The Unimodularity Theorem” of Oliver Knill , 2018, Linear Algebra and its Applications.

[9]  Oliver Knill,et al.  The Cohomology for Wu Characteristics , 2018, ArXiv.

[10]  Oliver Knill,et al.  Listening to the cohomology of graphs , 2018, ArXiv.

[11]  Oliver Knill,et al.  The strong ring of simplicial complexes , 2017, ArXiv.

[12]  Oliver Knill,et al.  On the arithmetic of graphs , 2017, ArXiv.

[13]  Oliver Knill,et al.  On a Dehn-Sommerville functional for simplicial complexes , 2017, ArXiv.

[14]  Oliver Knill,et al.  On Helmholtz free energy for finite abstract simplicial complexes , 2017, ArXiv.

[15]  Oliver Knill,et al.  Sphere geometry and invariants , 2017, ArXiv.

[16]  Oliver Knill,et al.  On Fredholm determinants in topology , 2016, ArXiv.

[17]  Oliver Knill,et al.  Gauss-Bonnet for multi-linear valuations , 2016, ArXiv.

[18]  Oliver Knill,et al.  Curvature from Graph Colorings , 2014, ArXiv.

[19]  A. Cabada Green’s Functions in the Theory of Ordinary Differential Equations , 2013 .

[20]  Oliver Knill,et al.  The McKean-Singer Formula in Graph Theory , 2013, ArXiv.

[21]  V. Yegnanarayanan,et al.  On product graphs , 2012 .

[22]  O. Knill A Brouwer fixed-point theorem for graph endomorphisms , 2012, ArXiv.

[23]  Oliver Knill,et al.  On index expectation and curvature for networks , 2012, ArXiv.

[24]  Oliver Knill,et al.  A graph theoretical Poincare-Hopf Theorem , 2012, ArXiv.

[25]  Oliver Knill,et al.  A graph theoretical Gauss-Bonnet-Chern Theorem , 2011, ArXiv.

[26]  W. Imrich,et al.  Handbook of Product Graphs, Second Edition , 2011 .

[27]  Oliver Knill,et al.  A discrete Gauss-Bonnet type theorem , 2010, 1009.2292.

[28]  J. Jonsson Simplicial complexes of graphs , 2007 .

[29]  Jozef Širáň,et al.  Landau's inequalities for tournament scores and a short proof of a theorem on transitive sub-tournaments , 2001 .

[30]  Shing-Tung Yau,et al.  Graph homotopy and Graham homotopy , 2001, Discret. Math..

[31]  Shing-Tung Yau,et al.  Discrete Green's Functions , 2000, J. Comb. Theory A.

[32]  W. Imrich,et al.  Product Graphs: Structure and Recognition , 2000 .

[33]  P. McMullen INTRODUCTION TO GEOMETRIC PROBABILITY , 1999 .

[34]  B. Simon,et al.  The xi function , 1996 .

[35]  Paolo M. Soardi,et al.  Potential Theory on Infinite Networks , 1994 .

[36]  Alexander V. Ivashchenko,et al.  Contractible transformations do not change the homology groups of graphs , 1994, Discret. Math..

[37]  Norman Levitt,et al.  The euler characteristic is the unique locally determined numerical homotopy invariant of finite complexes , 1992, Discret. Comput. Geom..

[38]  Jeremy Gray,et al.  A history of algebraic and differential topology, 1900–1960: By Jean Dieudonné. Boston and Basel (Birkhäuser). 1989. xxi + 648 pp , 1991 .

[39]  E. Spanier Algebraic Topology , 1990 .

[40]  J. Dieudonne,et al.  A History of Algebraic and Differential Topology, 1900 - 1960 , 1989 .

[41]  Jonathan L. Gross,et al.  Topological Graph Theory , 1987, Handbook of Graph Theory.

[42]  Hans L. Cycon,et al.  Schrodinger Operators: With Application to Quantum Mechanics and Global Geometry , 1987 .

[43]  R. Stanley,et al.  What Is Enumerative Combinatorics , 1986 .

[44]  I. Stakgold Green's Functions and Boundary Value Problems , 1979 .

[45]  P. Mani,et al.  Shellable Decompositions of Cells and Spheres. , 1971 .

[46]  Mary Ellen Rudin,et al.  An unshellable triangulation of a tetrahedron , 1958 .

[47]  G. Pólya An Elementary Analogue to the Gauss-Bonnet Theorem , 1954 .

[48]  Development of the concept of a complex for imitation and physical modeling of a hybrid power plant of a vehicle , 2020, Truck.

[49]  W. Hager,et al.  and s , 2019, Shallow Water Hydraulics.

[50]  Frank Harary,et al.  Graph Theory , 2016 .

[51]  O. Knill THE KÜNNETH FORMULA FOR GRAPHS , 2015 .

[52]  A. Encinas,et al.  THE CURL OF A WEIGHTED NETWORK , 2008 .

[53]  John M. Lee Introduction to Topological Manifolds , 2000 .

[54]  Andrew King,et al.  The Concept of a Manifold , 1999 .

[55]  Erhard Scholz,et al.  CHAPTER 2 – The Concept of Manifold, 1850–1950 , 1999 .

[56]  J. Zukas Introduction to the Modern Theory of Dynamical Systems , 1998 .

[57]  J. Yoccoz Introduction to Hyperbolic Dynamics , 1995 .

[58]  H. Weyl,et al.  Riemanns geometrische Ideen, ihre Auswirkung und ihre Verknüpfung mit der Gruppentheorie , 1988 .

[59]  H. Bigalke Heinrich Heesch : Kristallgeometrie, Parkettierungen, Vierfarbenforschung , 1988 .

[60]  O. Lanford,et al.  Introduction to Hyperbolic Sets , 1985 .

[61]  Eleftherios N. Economou,et al.  Green's functions in quantum physics , 1979 .

[62]  N. Biggs,et al.  Graph Theory 1736-1936 , 1976 .

[63]  C. R. F. Maunder Algebraic Topology , 1970 .

[64]  T. Banchoff CRITICAL POINTS AND CURVATURE FOR EMBEDDED POLYHEDRA , 1967 .

[65]  H. McKean,et al.  Curvature and the Eigenvalues of the Laplacian , 1967 .

[66]  W. T. Tutte Lectures on matroids , 1965 .

[67]  Gert Sabidussi,et al.  Graph multiplication , 1959 .

[68]  R. Bing A characterization of 3-space by partitionings , 1951 .

[69]  J. Whitehead Simplicial Spaces, Nuclei and m‐Groups , 1939 .

[70]  A. Tucker On Combinatorial Topology. , 1932, Proceedings of the National Academy of Sciences of the United States of America.