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Mark Grant

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    • 93 Citations
    20072020
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    Research Output 2007 2020

    • 93 Citations
    • 25 Article
    • 3 Conference contribution
    • 1 Book
    • 1 Chapter (peer-reviewed)
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    Article
    4 Citations (Scopus)
    4 Downloads (Pure)

    A mapping theorem for topological complexity

    Grant, M., Lupton, G. & Oprea, J., 19 Jun 2015, In : Algebraic & Geometric Topology. 15, 3, p. 1643-1666 24 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    Topological Complexity
    Theorem
    Rational Homotopy
    Lusternik-Schnirelmann Category
    Lower bound
    2 Citations (Scopus)

    An upper bound for topological complexity

    Farber, M., Grant, M., Lupton, G. & Oprea, J., 15 Mar 2019, In : Topology and its Applications. 255, p. 109-125 17 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    Topological Complexity
    Upper bound
    Invariant
    Universal Cover
    Simplicial Complex
    6 Citations (Scopus)

    Bordism groups of immersions and classes represented by self-intersections

    Eccles, P. J. & Grant, M., 2007, In : Algebraic & Geometric Topology. 7, p. 1081-1097 17 p.

    Research output: Contribution to journalArticle

    2 Citations (Scopus)
    20 Downloads (Pure)

    Bredon cohomology and robot motion planning

    Farber, M., Grant, M., Lupton, G. & Oprea, J., 16 Aug 2019, In : Algebraic & Geometric Topology. 19, 4, p. 2023-2059 37 p.

    Research output: Contribution to journalArticle

    Motion Planning
    Cohomology
    Robot
    Denote
    Torsion-free Group
    3 Downloads (Pure)

    Directed topological complexity of spheres

    Borat, A. & Grant, M., 7 Sep 2019, In : Journal of applied and computational topology. 7 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    Topological Complexity
    Homotopy Equivalence
    11 Citations (Scopus)

    Equivariant topological complexity

    Colman, H. & Grant, M., 8 Jan 2013, In : Algebraic & Geometric Topology. 12, 4, p. 2299-2316 18 p.

    Research output: Contribution to journalArticle

    1 Downloads (Pure)

    Homologies are infinitely complex

    Szucs, A. & Grant, M., Mar 2015, In : Topological Methods in Nonlinear Analysis. 45, 1, p. 55-62 8 p.

    Research output: Contribution to journalArticle

    Smooth Manifold
    Point Sets
    Codimension
    Homology
    Class

    Hopf Invariants for sectional category with applications to topological robotics

    González, J., Grant, M. & Vandembroucq, L., Dec 2019, In : Quarterly Journal of Mathematics. 70, 4, p. 1209-1252 43 p.

    Research output: Contribution to journalArticle

    Hopf Invariant
    Topological Complexity
    Robotics
    Lusternik-Schnirelmann Category
    Cell Complex

    Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity

    Angel, A., Colman, H., Grant, M. & Oprea, J., 11 Feb 2020, (Accepted/In press) In : Theory and Applications of Categories. 14 p.

    Research output: Contribution to journalArticle

    Lusternik-Schnirelmann Category
    Topological Complexity
    Equivariant
    Morita Equivalence
    Invariance
    7 Citations (Scopus)
    5 Downloads (Pure)

    New lower bounds for the topological complexity of aspherical spaces

    Grant, M., Lupton, G. & Oprea, J., 1 Jul 2015, In : Topology and its Applications. 189, p. 78-91 14 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    Topological Complexity
    Subgroup
    Lower bound
    Pi
    Cohomological Dimension
    2 Citations (Scopus)
    5 Downloads (Pure)

    On realizing homology classes by maps of restricted complexity

    Grant, M. & Szucs, A., Apr 2013, In : Bulletin of the London Mathematical Society. 45, 2, p. 329-340 12 p.

    Research output: Contribution to journalArticle

    Open Access
    File

    On Self-Intersection Invariants

    Grant, M., May 2013, In : Glasgow Mathematical Journal. 55, 2, p. 259-273 15 p.

    Research output: Contribution to journalArticle

    8 Downloads (Pure)

    Realizing homology classes up to cobordism

    Grant, M., Szűcs, A. & Terpai, T., Oct 2017, In : Osaka Journal of Mathematics. 54, 4, p. 801-805 5 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    Cobordism
    Immersion
    Homology
    Finite Set
    Sufficient
    11 Citations (Scopus)

    Robot motion planning, weights of cohomology classes, and cohomology operations

    Farber, M. & Grant, M., 2008, In : Proceedings of the American Mathematical Society. 136, 9, p. 3339-3349 11 p.

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Self-intersections of immersions and Steenrod operations

    Eccles, P. J. & Grant, M., Dec 2012, In : Acta Mathematica Hungarica. 137, 4, p. 272-281 10 p.

    Research output: Contribution to journalArticle

    9 Citations (Scopus)
    7 Downloads (Pure)

    Sequential motion planning of non-colliding particles in Euclidean spaces

    Gonzalez, J. & Grant, M., 2015, In : Proceedings of the American Mathematical Society. 143, 10, p. 4503-4512 10 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    Motion Planning
    Motion planning
    Euclidean space
    Topological Complexity
    Robotics
    11 Citations (Scopus)

    Spaces of topological complexity one

    Grant, M., Lupton, G. & Oprea, J., 2013, In : Homology, Homotopy and Applications. 15, 2, p. 73-81 9 p.

    Research output: Contribution to journalArticle

    6 Downloads (Pure)

    Symmetrized topological complexity

    Grant, M., 1 Jun 2019, In : Journal of Topology and Analysis. 11, 2, p. 387-403 17 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    Topological Complexity
    Obstruction Theory
    Equivariant
    Cohomology
    Upper and Lower Bounds
    1 Citation (Scopus)
    3 Downloads (Pure)

    The Poincaré-Hopf Theorem for line fields revisited

    Crowley, D. & Grant, M., Jul 2017, In : Journal of Geometry and Physics. 117, p. 187-196 10 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    theorems
    Line
    Singularity
    Theorem
    differential geometry

    The Topological Period-Index Conjecture for spinc 6-manifolds

    Crowley, D. J. & Grant, M., 26 Feb 2020, (Accepted/In press) In : Annals of K-Theory. 17 p.

    Research output: Contribution to journalArticle

    Brauer Group
    Function Fields
    Analogue
    9 Citations (Scopus)

    Topological complexity, fibrations and symmetry

    Grant, M., 1 Jan 2012, In : Topology and its Applications. 159, 1, p. 88-97 10 p.

    Research output: Contribution to journalArticle

    Open Access
    13 Citations (Scopus)

    Topological Complexity of Configuration Spaces

    Farber, M. & Grant, M., May 2009, In : Proceedings of the American Mathematical Society. 137, 5, p. 1841-1847 8 p.

    Research output: Contribution to journalArticle

    Topological complexity of motion planning and Massey products

    Grant, M., 2009, In : Banach Center Publications. 85, p. 193-203 11 p.

    Research output: Contribution to journalArticle

    File
    Topological Complexity
    Motion Planning
    Fibration
    Genus
    Zero-divisor
    2 Citations (Scopus)

    Topological complexity of motion planning in projective product spaces

    Gonzalez, J., Grant, M., Torres-Giese, E. & Xicotencatl, M., 8 Apr 2013, In : Algebraic & Geometric Topology. 13, 2, p. 1027-1047 21 p.

    Research output: Contribution to journalArticle

    1 Downloads (Pure)

    Topological complexity of symplectic manifolds

    Grant, M. & Mescher, S., 3 Aug 2019, In : Mathematische Zeitschrift. 13 p.

    Research output: Contribution to journalArticle

    Open Access
    File
    Topological Complexity
    Symplectic Manifold
    Fundamental Group
    Lusternik-Schnirelmann Category
    Hyperbolic Groups